Combinations of beta-lactam compounds and probenecid and uses thereof

ABSTRACT

The present disclosure relates to combinations of a β-lactam compound or a pharmaceutically acceptable salt thereof and probenecid or a pharmaceutically acceptable salt thereof. The present disclosure also relates to methods of treating or preventing a disease via administering to subjects in need thereof a β-lactam compound or a pharmaceutically acceptable salt thereof and probenecid or a pharmaceutically acceptable salt thereof.

RELATED APPLICATIONS

This application claims priority to, and the benefit of, U.S.Provisional Application Nos. 62/804,970, filed Feb. 13, 2019, and62/682,116, filed Jun. 7, 2018, the entire contents of each of which areincorporated herein by reference.

BACKGROUND

β-lactam compounds are a class of antibiotics having a beta-lactam ringin their molecular structures. β-lactam compounds have been used in thetreatment of diseases associated with Gram-positive and Gram-negativebacteria. The mechanism of action of these β-lactam compounds requires,optimally, that concentrations of the antibiotic remain at or above acertain inhibitory threshold, known as the ‘mean inhibitoryconcentration (MIC)’ in order to be effective. Keeping these antibioticconcentrations elevated also helps avoid the potential for antibacterialresistance due to the selection of bacteria with higher MIC's. There is,therefore, a need for compositions and methods related to β-lactamantibiotics that optimize their tissue concentrations in order toimprove their ability to control an infection as well as alleviate oreliminate the potential for antibiotic resistance.

SUMMARY

The present disclosure provides, inter alia, a method of treating orpreventing a disease, comprising administering to a subject in needthereof a pharmaceutically effective amount of a β-lactam compound or apharmaceutically acceptable salt thereof and probenecid or apharmaceutically acceptable salt thereof, wherein the β-lactam compoundor the pharmaceutically acceptable salt thereof and probenecid or thepharmaceutically acceptable salt thereof are administered by the sameadministration route.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered simultaneously.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered by enteral administration.

In some embodiments, the enteral administration is oral administration.

In some embodiments, an oral co-formulation comprising the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof is administered.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered in separate oralformulations.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that issubstantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid by different administration routes; and

a plasma concentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that issubstantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes.

In some aspects, the present disclosure provides, a method of treatingor preventing a disease, comprising administering to a subject in needthereof a pharmaceutically effective amount of a β-lactam compound or apharmaceutically acceptable salt thereof and probenecid or apharmaceutically acceptable salt thereof over a period of time, whereinthe administration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides a β-lactam compound ora pharmaceutically acceptable salt thereof for use in combination withprobenecid or a pharmaceutically acceptable salt thereof in treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides probenecid or apharmaceutically acceptable salt thereof for use in combination with aβ-lactam compound or a pharmaceutically acceptable salt thereof intreating or preventing a disease in a subject in need thereof, whereinthe β-lactam compound or the pharmaceutically acceptable salt thereofand probenecid or the pharmaceutically acceptable salt thereof areadministered to the subject by the same administration route.

In some aspects, the present disclosure provides a combination of aβ-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof for use intreating or preventing a disease in a subject in need thereof, whereinthe β-lactam compound or the pharmaceutically acceptable salt thereofand probenecid or the pharmaceutically acceptable salt thereof areadministered to the subject by the same administration route.

In some aspects, the present disclosure provides use of a β-lactamcompound in combination with probenecid or a pharmaceutically acceptablesalt thereof in the manufacture of a medicament for treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides use of probenecid incombination with a β-lactam compound or a pharmaceutically acceptablesalt thereof in the manufacture of a medicament for treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides use of a combination ofa β-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease in asubject in need thereof, wherein the β-lactam compound or thepharmaceutically acceptable salt thereof and probenecid or thepharmaceutically acceptable salt thereof are administered to the subjectby the same administration route.

In some aspects, the present disclosure provides a β-lactam compound ora pharmaceutically acceptable salt thereof for use in combination withprobenecid or a pharmaceutically acceptable salt thereof in treating orpreventing a disease, wherein: the β-lactam compound or thepharmaceutically acceptable salt thereof and the probenecid or apharmaceutically acceptable salt thereof are administered to a subjectin need over a period of time, wherein the administration results in aplasma concentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides probenecid or apharmaceutically acceptable salt thereof for use in combination with aβ-lactam compound or a pharmaceutically acceptable salt thereof intreating or preventing a disease, wherein:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides a combination of aβ-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof for use intreating or preventing a disease, wherein:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of a β-lactamcompound or a pharmaceutically acceptable salt thereof in combinationwith probenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of probenecid or apharmaceutically acceptable salt thereof in combination with a β-lactamcompound or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of a combination ofa β-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) for the β-lactam compound thatis higher in the subject in need thereof as compared to the comparablesubject being administered to the pharmaceutically effective amount ofthe β-lactam compound without probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides a pharmaceuticalcomposition comprising a β-lactam compound or a pharmaceuticallyacceptable salt thereof and probenecid or a pharmaceutically acceptablesalt thereof.

In some aspects, the present disclosure provides a pharmaceutical kitcomprising a β-lactam compound or a pharmaceutically acceptable saltthereof in a first package and probenecid or a pharmaceuticallyacceptable salt thereof in a second package.

In some aspects, the present disclosure provides a compound or apharmaceutical salt thereof, wherein administration of the compound orthe pharmaceutical salt thereof in combination with probenecid or apharmaceutically acceptable salt thereof into a subject in need thereofover a period of time results in a plasma concentration versus timecurve for the compound having: an area under the curve (AUC) that ishigher in the subject in need thereof as compared to a comparablesubject being administered to the pharmaceutically effective amount ofthe compound without probenecid over the period of time,

a maximum plasma concentration (C_(max)) for the compound that is higherin the subject in need thereof as compared to the comparable subjectbeing administered to the pharmaceutically effective amount of thecompound without probenecid over the period of time, or

a combination thereof.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this disclosure belongs. In the specification, thesingular forms also include the plural unless the context clearlydictates otherwise. Although methods and materials similar or equivalentto those described herein can be used in the practice or testing of thepresent disclosure, suitable methods and materials are described below.All publications, patent applications, patents and other referencesmentioned herein are incorporated by reference. The references citedherein are not admitted to be prior art to the claimed invention. In thecase of conflict, the present specification, including definitions, willcontrol. In addition, the materials, methods and examples areillustrative only and are not intended to be limiting. In the case ofconflict between the chemical structures and names of the compoundsdisclosed herein, the chemical structures will control.

Other features and advantages of the disclosure will be apparent fromthe following detailed description and claims.

BRIEF DESCRIPTION OF DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 is a graph showing the effect of probenecid on the area under thecurve (AUC) of sulopenem in the plasma when delivered through the oralroute with an oral sulopenem prodrug.

FIG. 2 is a diagram showing the effect of administrating the β-lactamcompound (Compound III-2b) and probencid in the fasted state on theplasma level of the β-lactam compound (Compound IIb).

FIG. 3 is a diagram showing the effect of administrating the β-lactamcompound (Compound III-2b) and probencid in the fed state on the plasmalevel of the β-lactam compound (Compound IIb).

FIG. 4 is a graph showing the effect of administering a β-lactamcompound (Compound III-2b) and probenecid by the same administrationroute (as compared to by different administration routes) on the areaunder the curve (AUC) for the β-lactam compound (Compound IIb).

FIG. 5 is a graph showing the effect of administering a β-lactamcompound (Compound III-2b) and probenecid by the same administrationroute (as compared to by different administration routes) on the maximumplasma concentration (C_(max)) for the β-lactam compound (CompoundIII-2b).

DETAILED DESCRIPTION

The present disclosure provides, inter alia, a method of treating orpreventing a disease, comprising administering to a subject in needthereof a pharmaceutically effective amount of a β-lactam compound or apharmaceutically acceptable salt thereof and probenecid or apharmaceutically acceptable salt thereof, wherein the β-lactam compoundor the pharmaceutically acceptable salt thereof and probenecid or thepharmaceutically acceptable salt thereof are administered by the sameadministration route.

In some aspects, the present disclosure provides a method of treating orpreventing a disease, comprising administering to a subject in needthereof a pharmaceutically effective amount of a β-lactam compound or apharmaceutically acceptable salt thereof and probenecid or apharmaceutically acceptable salt thereof over a period of time, whereinthe administration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some embodiments, the period of the time is longer than about 24hours.

In some embodiments, the period of the time ranges from about 2 days toabout 30 days, from about 3 days to about 20 days, from about 4 days toabout 15 days, from about 5 days to about 10 days, or from about 6 daysto about 8 days.

In some embodiments, the period of the time is about 7 days.

Effects on the AUC and/or C_(max)

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes by about 5% or greater,about 10% or greater, about 15% or greater, about 20% or greater, about25% or greater, about 30% or greater, about 40% or greater, about 50% orgreater, about 60% or greater, about 80% or greater, about 100% orgreater, about 150% or greater, about 200% or greater, about 300% orgreater, about 400% or greater, or about 500% or greater within about 30minutes, about 1 hour, about 2 hours, about 3 hours, about 6 hours,about 12 hours, about 18 hours, about 1 day, about 2 days, about 3 days,about 4 days, about 5 days, about 6 days, or about 7 days from theadministration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes about 10% or greater,about 15% or greater, about 20% or greater, about 25% or greater, orabout 30% or greater within about 12 hours, about 18 hours, about 1 day,about 2 days, or about 3 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes about 15% or greater,about 20% or greater, or about 25% or greater within about 18 hours,about 1 day, or about 2 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes about 15% or greater,about 20% or greater, or about 25% or greater within about 18 hours fromthe administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes about 15% or greater,about 20% or greater, or about 25% or greater within about 1 day fromthe administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes about 15% or greater,about 20% or greater, or about 25% or greater within about 2 days fromthe administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes by about 20% or greaterwithin about 1 day from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that is fromabout 50% to about 150%, from about 60% to about 140%, from about 70% toabout 130%, from about 80% to about 120%, from about 90% to about 110%,from about 95% to about 105%, or from 98% to about 102% as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that is fromabout 70% to about 130%, from about 80% to about 120%, from about 90% toabout 110%, from about 95% to about 105%, or from 98% to about 102% ascompared to a comparable subject being administered with the β-lactamcompound and probenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that is fromabout 90% to about 110%, from about 95% to about 105%, or from 98% toabout 102% as compared to a comparable subject being administered withthe β-lactam compound and probenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that is fromabout 95% to about 105%, or from 98% to about 102% as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that is from 98%to about 102% as compared to a comparable subject being administeredwith the β-lactam compound and probenecid by different administrationroutes.

In some embodiments, administration results in a plasma concentrationfor the β-lactam compound having a maximum plasma concentration(C_(max)) in the subject in need thereof that is substantially the sameas compared to a comparable subject being administered with the β-lactamcompound and probenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid by different administration routes; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid by different administration routes byabout 5% or greater, about 10% or greater, about 15% or greater, about20% or greater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid by different administration routes byabout 5% or greater, about 10% or greater, about 15% or greater, about20% or greater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is from about 50% to about 150%, from about 60% to about 140%, fromabout 70% to about 130%, from about 80% to about 120%, from about 90% toabout 110%, from about 95% to about 105%, or from 98% to about 102% ascompared to a comparable subject being administered with the β-lactamcompound and probenecid by different administration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid by different administration routes byabout 5% or greater, about 10% or greater, about 15% or greater, about20% or greater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid in separate formulations by about 5% orgreater, about 10% or greater, about 15% or greater, about 20% orgreater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid in separate formulations by about 5% orgreater, about 10% or greater, about 15% or greater, about 20% orgreater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is from about 50% to about 150%, from about 60% to about 140%, fromabout 70% to about 130%, from about 80% to about 120%, from about 90% toabout 110%, from about 95% to about 105%, or from 98% to about 102% ascompared to a comparable subject being administered with the β-lactamcompound and probenecid in separate formulations.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid in separate formulations by about 5% orgreater, about 10% or greater, about 15% or greater, about 20% orgreater, about 25% or greater, about 30% or greater, about 40% orgreater, about 50% or greater, about 60% or greater, about 80% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid in separateformulations.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid without food (e.g., the comparablesubject is fasted) by about 5% or greater, about 10% or greater, about15% or greater, about 20% or greater, about 25% or greater, about 30% orgreater, about 40% or greater, about 50% or greater, about 60% orgreater, about 80% or greater, about 100% or greater, about 150% orgreater, about 200% or greater, about 300% or greater, about 400% orgreater, or about 500% or greater within about 30 minutes, about 1 hour,about 2 hours, about 3 hours, about 6 hours, about 12 hours, about 18hours, about 1 day, about 2 days, about 3 days, about 4 days, about 5days, about 6 days, or about 7 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid without food (e.g., the comparablesubject is fasted) by about 5% or greater, about 10% or greater, about15% or greater, about 20% or greater, about 25% or greater, about 30% orgreater, about 40% or greater, about 50% or greater, about 60% orgreater, about 80% or greater, about 100% or greater, about 150% orgreater, about 200% or greater, about 300% or greater, about 400% orgreater, or about 500% or greater within about 30 minutes, about 1 hour,about 2 hours, about 3 hours, about 6 hours, about 12 hours, about 18hours, about 1 day, about 2 days, about 3 days, about 4 days, about 5days, about 6 days, or about 7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is from about 50% to about 150%, from about 60% to about 140%, fromabout 70% to about 130%, from about 80% to about 120%, from about 90% toabout 110%, from about 95% to about 105%, or from 98% to about 102% ascompared to a comparable subject being administered with the β-lactamcompound and probenecid without food (e.g., the comparable subject isfasted).

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with theβ-lactam compound and probenecid without food (e.g., the comparablesubject is fasted) by about 5% or greater, about 10% or greater, about15% or greater, about 20% or greater, about 25% or greater, about 30% orgreater, about 40% or greater, about 50% or greater, about 60% orgreater, about 80% or greater, about 100% or greater, about 150% orgreater, about 200% or greater, about 300% or greater, about 400% orgreater, or about 500% or greater within about 30 minutes, about 1 hour,about 2 hours, about 3 hours, about 6 hours, about 12 hours, about 18hours, about 1 day, about 2 days, about 3 days, about 4 days, about 5days, about 6 days, or about 7 days from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid without food(e.g., the comparable subject is fasted).

In some embodiments, about 500-400 mg, about 500±300 mg, about 500-200mg, about 500±100 mg, about 500-90 mg, about 500-80 mg, about 500-70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the β-lactam compound (e.g., Compound III-2b) or the pharmaceuticallyacceptable salt and about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the probenecid or the pharmaceutically acceptable salt areadministered to the subject in need thereof by the same administrationroute, and the administration results in a plasma concentration for theβ-lactam compound having: an area under the curve (AUC) being from about4325±3000 ng·h/mL, about 4325±2500 ng·h/mL, about 4325±2000 ng·h/mL,about 4325±1500 ng·h/mL, about 4325±1000 ng·h/mL, about 4325±900ng·h/mL, about 4325±800 ng·h/mL, about 4325±700 ng·h/mL, about 4325±600ng·h/mL, about 4325±500 ng·h/mL, about 4325±400 ng·h/mL, about 4325±300ng·h/mL, about 4325±200 ng·h/mL, about 4325±100 ng·h/mL, about 4325±90ng·h/mL, about 4325±80 ng·h/mL, about 4325±70 ng·h/mL, about 4325±60ng·h/mL, about 4325±50 ng·h/mL, about 4325±40 ng·h/mL, about 4325±30ng·h/mL, about 4325±20 ng·h/mL, or about 4325±10 ng·h/mL (e.g., about4325 ng·h/mL) within about 1 day from the administration.

In some embodiments, about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the β-lactam compound (e.g., Compound III-2b) or the pharmaceuticallyacceptable salt and about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the probenecid or the pharmaceutically acceptable salt areadministered to the subject in need thereof by the same administrationroute and with food (e.g., the subject is fed), and the administrationresults in a plasma concentration for the β-lactam compound having:

an area under the curve (AUC) being from about 6600±3000 ng·h/mL, about6600±2500 ng·h/mL, about 6600±2000 ng·h/mL, about 6600±1500 ng·h/mL,about 6600±1000 ng·h/mL, about 6600±900 ng·h/mL, about 6600±800 ng·h/mL,about 6600±700 ng·h/mL, about 6600±600 ng·h/mL, about 6600±500 ng·h/mL,about 6600±400 ng·h/mL, about 6600±300 ng·h/mL, about 6600±200 ng·h/mL,about 6600±100 ng·h/mL, about 6600±90 ng·h/mL, about 6600±80 ng·h/mL,about 6600±70 ng·h/mL, about 660060 ng·h/mL, about 6600±50 ng·h/mL,about 6600±40 ng·h/mL, about 6600±30 ng·h/mL, about 6600±20 ng·h/mL, orabout 6600±10 ng·h/mL (e.g., about 6600 ng·h/mL) within about 1 day fromthe administration.

In some embodiments, about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 50060 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg, about500±20 mg, about 50010 mg, or about 500±5 mg (e.g., about 500 mg) of theβ-lactam compound (e.g., Compound III-2b) or the pharmaceuticallyacceptable salt and about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 50010 mg, or about 500±5 mg (e.g., about 500 mg)of the probenecid or the pharmaceutically acceptable salt areadministered to the subject in need thereof in a co-formulation, and theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) being from about 5100±3000 ng·h/mL, about5100±2500 ng·h/mL, about 5100±2000 ng·h/mL, about 5100±1500 ng·h/mL,about 5100±1000 ng·h/mL, about 5100±900 ng·h/mL, about 5100±800 ng·h/mL,about 5100±700 ng·h/mL, about 5100±600 ng·h/mL, about 5100±500 ng·h/mL,about 5100±400 ng·h/mL, about 5100±300 ng·h/mL, about 5100±200 ng·h/mL,about 5100±100 ng·h/mL, about 5100±90 ng·h/mL, about 5100±80 ng·h/mL,about 5100±70 ng·h/mL, about 5100±60 ng·h/mL, about 5100±50 ng·h/mL,about 5100±40 ng·h/mL, about 5100±30 ng·h/mL, about 5100±20 ng·h/mL, orabout 5100±10 ng·h/mL (e.g., about 5100 ng·h/mL) within about 1 day fromthe administration.

In some embodiments, about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the β-lactam compound (e.g., Compound III-2b) or the pharmaceuticallyacceptable salt and about 500±400 mg, about 500±300 mg, about 500±200mg, about 500±100 mg, about 500±90 mg, about 500±80 mg, about 500±70 mg,about 500±60 mg, about 500±50 mg, about 500±40 mg, about 500±30 mg,about 500±20 mg, about 500±10 mg, or about 500±5 mg (e.g., about 500 mg)of the probenecid or the pharmaceutically acceptable salt areadministered to the subject in need thereof in a co-formulation and withfood (e.g., the subject is fed), and the administration results in aplasma concentration for the β-lactam compound having: an area under thecurve (AUC) being from about 7340±3000 ng·h/mL, about 7340±2500 ng·h/mL,about 7340±2000 ng·h/mL, about 7340±1500 ng·h/mL, about 7340±1000ng·h/mL, about 7340±900 ng·h/mL, about 7340±800 ng·h/mL, about 7340±700ng·h/mL, about 7340±600 ng·h/mL, about 7340±500 ng·h/mL, about 7340±400ng·h/mL, about 7340±300 ng·h/mL, about 7340±200 ng·h/mL, about 7340±100ng·h/mL, about 7340±90 ng·h/mL, about 7340±80 ng·h/mL, about 7340±70ng·h/mL, about 7340±60 ng·h/mL, about 7340±50 ng·h/mL, about 7340±40ng·h/mL, about 7340±30 ng·h/mL, about 7340±20 ng·h/mL, or about 7340±10ng·h/mL (e.g., about 7340 ng·h/mL) within about 1 day from theadministration.

In some embodiments, about 500 mg of the β-lactam compound or thepharmaceutically acceptable salt and about 500 mg of the probenecid orthe pharmaceutically acceptable salt are administered to the subject inneed thereof, and the administration results in a plasma concentrationfor the β-lactam compound having:

an area under the curve (AUC) being from about 4100 ng·h/mL to about5500 ng·h/mL, from about 4200 ng·h/mL to about 5400 ng·h/mL, from about4300 ng·h/mL to about 5300 ng·h/mL, from about 4400 ng·h/mL to about5200 ng·h/mL, from about 4500 ng·h/mL to about 5100 ng·h/mL, from about4650 ng·h/mL to about 5000 ng·h/mL, from about 4750 ng·h/mL to about4900 ng·h/mL, or from about 4800 ng·h/mL to about 4850 ng·h/mL withinabout 12 hours from the administration; and

a maximum plasma concentration (C_(max)) being from about 1100 ng/mL toabout 2500 ng/mL, from about 1200 ng/mL to about 2400 ng/mL, from about1300 ng/mL to about 2300 ng/mL, from about 1400 ng/mL to about 2200ng/mL, from about 1500 ng/mL to about 2100 ng/mL, from about 1650 ng/mLto about 2000 ng/mL, from about 1750 ng/mL to about 1900 ng/mL, or fromabout 1800 ng/mL to about 1850 ng/mL.

In some embodiments, about 500 mg of the β-lactam compound or thepharmaceutically acceptable salt and about 500 mg of the probenecid orthe pharmaceutically acceptable salt are administered to the subject inneed thereof, and the administration results in a plasma concentrationfor the β-lactam compound having:

an area under the curve (AUC) being from about 7000 ng·h/mL to about8400 ng·h/mL, from about 7100 ng·h/mL to about 8300 ng·h/mL, from about7200 ng·h/mL to about 8200 ng·h/mL, from about 7300 ng·h/mL to about5100 ng·h/mL, from about 7450 ng·h/mL to about 8100 ng·h/mL, from about7500 ng·h/mL to about 8050 ng·h/mL, or from about 7550 ng·h/mL to about8000 ng·h/mL within about 12 hours from the administration; and

a maximum plasma concentration (C_(max)) being from about 2100 ng/mL toabout 3300 ng/mL, from about 2200 ng/mL to about 3200 ng/mL, from about2300 ng/mL to about 3100 ng/mL, from about 2400 ng/mL to about 3000ng/mL, from about 2500 ng/mL to about 2900 ng/mL, from about 2550 ng/mLto about 2800 ng/mL, from about 2600 ng/mL to about 2750 ng/mL, or fromabout 2650 ng/mL to about 2700 ng/mL.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted).

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) byabout 5% or greater, about 10% or greater, about 20% or greater, about30% or greater, about 40% or greater, about 50% or greater, about 55% orgreater, about 60% or greater, about 65% or greater, about 70% orgreater, about 100% or greater, about 150% or greater, about 200% orgreater, about 300% or greater, about 400% or greater, or about 500% orgreater within about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 6 hours, about 12 hours, about 18 hours, about 1 day, about2 days, about 3 days, about 4 days, about 5 days, about 6 days, or about7 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) about50% or greater, about 55% or greater, about 60% or greater, about 65% orgreater, or about 70% or greater within about 12 hours, about 18 hours,about 1 day, about 2 days, or about 3 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) about55% or greater, about 60% or greater, or about 65% or greater withinabout 12 hours, about 1 day, or about 2 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) about55% or greater, about 60% or greater, or about 65% or greater withinabout 12 hours from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) about55% or greater, about 60% or greater, or about 65% or greater withinabout 1 day from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) about55% or greater, about 60% or greater, or about 65% or greater withinabout 2 days from the administration.

In some embodiments, the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid without food (e.g., the comparable subject is fasted) byabout 60% or greater within about 1 day from the administration.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound in the subject in need thereofis observed at a time being after about the first 24 hours of theadministration.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound in the subject in need thereofis observed at a time being after about first 2 days and within aboutfirst 30 days, after about first 3 days and within about first 20 days,after about first 4 days and within about first 15 days, after aboutfirst 5 days and within about first 10 days, or after about first 6 daysand within about first 8 days of the administration.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound in the subject in need thereofis observed at a time being about the 7th day of the administration.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound in the subject in need thereofis observed at a time being after about the first 24 hours of theadministration, and being on or before about the 30th day, about the20th day, about the 15th day, about the 10th day, about the 8th day, orabout the 7th of the administration.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound in the comparable subject islower at the end of the period of the time as compared to the first dayof the administration, preferably, by an amount ranging from about 1% toabout 60%, from about 3% to about 50%, from about 5% to about 40%, fromabout 8% to about 38%, or from about 10% to about 35%.

In some embodiments, one or both of the AUC and C_(max) of the plasmaconcentration for the β-lactam compound is higher in the subject in needthereof at the end of the period of the time as compared to thecomparable subject at the first day of the administration, preferably,by an amount ranging from about 2% to about 100%, from about 4% to about80%, from about 6% to about 60%, from about 8% to about 40%, from about10% to about 30%, from about 12% to about 25%, or from about 15% toabout 20%.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration ranges from about 1.5 ng/mL to about 2.5 ng/mL, fromabout 1.6 ng/mL to about 2.4 ng/mL, from about 1.7 ng/mL to about 2.3ng/mL, from about 1.8 ng/mL to about 2.2 ng/mL, or from about 1.9 ng/mLto about 2.1 ng/mL per mg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration is at about 2.0 ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration ranges from about 0.7 ng/mL to about 1.8 ng/mL,from about 0.8 ng/mL to about 1.7 ng/mL, from about 0.9 ng/mL to about1.6 ng/mL, from about 1.0 ng/mL to about 1.5 ng/mL, from about 1.1 ng/mLto about 1.4 ng/mL, or from about 1.2 ng/mL to about 1.3 ng/mL per mg ofβ-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration is at about 1.25 ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration ranges from about 1.6 ng/mL to about 2.7ng/mL, from about 1.7 ng/mL to about 2.6 ng/mL, from about 1.8 ng/mL toabout 2.5 ng/mL, from about 1.9 ng/mL to about 2.4 ng/mL, from about 2.0ng/mL to about 2.3 ng/mL, or from about 2.1 ng/mL to about 2.2 ng/mL permg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 2.15 ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration ranges from about 1.6 ng/mL to about 2.7ng/mL, from about 1.7 ng/mL to about 2.6 ng/mL, from about 1.8 ng/mL toabout 2.5 ng/mL, from about 1.9 ng/mL to about 2.4 ng/mL, from about 2.0ng/mL to about 2.3 ng/mL, or from about 2.1 ng/mL to about 2.2 ng/mL permg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration is at about 2.15 ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration ranges from about 1.2 ng/mL to about 2.2 ng/mL, fromabout 1.3 ng/mL to about 2.1 ng/mL, from about 1.4 ng/mL to about 2.0ng/mL, from about 1.5 ng/mL to about 1.9 ng/mL, or from about 1.6 ng/mLto about 1.8 ng/mL per mg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration is at about 1.7 ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration ranges from about 0.8 ng/mL to about 1.8 ng/mL,from about 0.9 ng/mL to about 1.7 ng/mL, from about 1.0 ng/mL to about1.6 ng/mL, from about 1.1 ng/mL to about 1.5 ng/mL, or from about 1.2ng/mL to about 1.4 ng/mL per mg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration is at about 1.3 ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration ranges from about 1.2 ng/mL to about 2.2ng/mL, from about 1.3 ng/mL to about 2.1 ng/mL, from about 1.4 ng/mL toabout 2.0 ng/mL, from about 1.5 ng/mL to about 1.9 ng/mL, or from about1.6 ng/mL to about 1.8 ng/mL per mg of β-lactam compound administereddaily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 1.7 ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration ranges from about 0.9 ng/mL to about 2.0ng/mL, from about 1.0 ng/mL to about 1.9 ng/mL, from about 1.1 ng/mL toabout 1.8 ng/mL, from about 1.2 ng/mL to about 1.7 ng/mL, from about 1.3ng/mL to about 1.6 ng/mL, or from about 1.4 ng/mL to about 1.5 ng/mL permg of β-lactam compound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration is at about 1.45 ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration from about 2.5 hr·ng/mL to about 3.2 hr·ng/mL, from about2.6 hr·ng/mL to about 3.1 hr·ng/mL, from about 2.7 hr·ng/mL to about 3.0hr·ng/mL, or from about 2.8 hr·ng/mL to about 2.9 hr·ng/mL per mg ofβ-lactam compound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 2.85 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration ranges from about 1.6 hr·ng/mL to about 2.2 hr·ng/mL,from about 1.7 hr·ng/mL to about 2.1 hr·ng/mL, or from about 1.8hr·ng/mL to about 2.0 hr·ng/mL per mg of β-lactam compound administereddaily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 1.9 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration ranges from about 3.9 hr·ng/mL to about 4.5 hr·ng/mL,from about 4.0 hr·ng/mL to about 4.4 hr·ng/mL, or from about 4.1hr·ng/mL to about 4.3 hr·ng/mL per mg of β-lactam compound administereddaily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 4.2 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration ranges from about 4.1 hr·ng/mL to about 4.7hr·ng/mL, from about 4.2 hr·ng/mL to about 4.6 hr·ng/mL, or from about4.3 hr·ng/mL to about 4.5 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration the resulted AUC is at about 4.4 hr·ng/mL per mgof β-lactam compound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration ranges from about 3.2 hr·ng/mL to about 4.0 hr·ng/mL,from about 3.3 hr·ng/mL to about 3.9 hr·ng/mL, from about 3.4 hr·ng/mLto about 3.8 hr·ng/mL, or from about 3.5 hr·ng/mL to about 3.7 hr·ng/mLper mg of β-lactam compound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 3.6 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration ranges from about 2.2 hr·ng/mL to about 3.1 hr·ng/mL,from about 2.3 hr·ng/mL to about 3.0 hr·ng/mL, from about 2.4 hr·ng/mLto about 2.9 hr·ng/mL, from about 2.5 hr·ng/mL to about 2.8 hr·ng/mL, orfrom about 2.6 hr·ng/mL to about 2.7 hr·ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 2.65 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration ranges from about 3.4 hr·ng/mL to about 4.3 hr·ng/mL,from about 3.5 hr·ng/mL to about 4.2 hr·ng/mL, from about 3.6 hr·ng/mLto about 4.1 hr·ng/mL, from about 3.7 hr·ng/mL to about 4.0 hr·ng/mL, orfrom about 3.8 hr·ng/mL to about 3.9 hr·ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 3.85 hr·ng/mL per mg of β-lactam compoundadministered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration ranges from about 3.9 hr·ng/mL to about 4.7hr·ng/mL, from about 4.0 hr·ng/mL to about 4.6 hr·ng/mL, from about 4.1hr·ng/mL to about 4.4 hr·ng/mL, from about 4.2 hr·ng/mL to about 4.3hr·ng/mL per mg of β-lactam compound administered daily.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 4.25 hr·ng/mL per mg of β-lactamcompound administered daily.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration is at about 0.5 ng/mL, about 0.55 ng/mL, about 0.6ng/mL, about 0.65 ng/mL, about 0.7 ng/mL, about 0.75 ng/mL, about 0.8ng/mL, about 0.85 ng/mL, about 0.9 ng/mL, about 0.95 ng/mL, about 1ng/mL, about 1.05 ng/mL, about 1.1 ng/mL, about 1.15 ng/mL, about 1.2ng/mL, about 1.25 ng/mL, about 1.3 ng/mL, about 1.35 ng/mL, about 1.4ng/mL, about 1.45 ng/mL, about 1.5 ng/mL, about 1.55 ng/mL, about 1.6ng/mL, about 1.65 ng/mL, about 1.7 ng/mL, about 1.75 ng/mL, about 1.8ng/mL, about 1.85 ng/mL, about 1.9 ng/mL, about 1.95 ng/mL, about 2ng/mL, about 2.05 ng/mL, about 2.1 ng/mL, about 2.15 ng/mL, about 2.2ng/mL, about 2.25 ng/mL, about 2.3 ng/mL, about 2.35 ng/mL, about 2.4ng/mL, about 2.45 ng/mL, about 2.5 ng/mL, about 2.55 ng/mL, about 2.6ng/mL, about 2.65 ng/mL, about 2.7 ng/mL, about 2.75 ng/mL, about 2.8ng/mL, about 2.85 ng/mL, about 2.9 ng/mL, about 2.95 ng/mL, about 3ng/mL, about 3.1 ng/mL, about 3.2 ng/mL, about 3.3 ng/mL, about 3.4ng/mL, about 3.5 ng/mL, about 3.6 ng/mL, about 3.7 ng/mL, about 3.8ng/mL, about 3.9 ng/mL, about 4 ng/mL, about 4.1 ng/mL, about 4.2 ng/mL,about 4.3 ng/mL, about 4.4 ng/mL, about 4.5 ng/mL, about 4.6 ng/mL,about 4.7 ng/mL, about 4.8 ng/mL, about 4.9 ng/mL, about 5 ng/mL, about5.5 ng/mL, about 6 ng/mL, about 6.5 ng/mL, about 7 ng/mL, about 7.5ng/mL, about 8 ng/mL, about 8.5 ng/mL, about 9 ng/mL, about 9.5 ng/mL,about 10 ng/mL, about 11 ng/mL, about 12 ng/mL, about 13 ng/mL, about 14ng/mL, about 15 ng/mL, about 16 ng/mL, about 17 ng/mL, about 18 ng/mL,about 19 ng/mL, about 20 ng/mL, about 25 ng/mL, about 30 ng/mL, about 35ng/mL, about 40 ng/mL, about 45 ng/mL, about 50 ng/mL, about 60 ng/mL,about 70 ng/mL, about 80 ng/mL, about 90 ng/mL, or about 100 ng/mL permg of β-lactam compound administered daily, or any range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration is at about 0.5 ng/mL, about 0.55 ng/mL, about 0.6ng/mL, about 0.65 ng/mL, about 0.7 ng/mL, about 0.75 ng/mL, about 0.8ng/mL, about 0.85 ng/mL, about 0.9 ng/mL, about 0.95 ng/mL, about 1ng/mL, about 1.05 ng/mL, about 1.1 ng/mL, about 1.15 ng/mL, about 1.2ng/mL, about 1.25 ng/mL, about 1.3 ng/mL, about 1.35 ng/mL, about 1.4ng/mL, about 1.45 ng/mL, about 1.5 ng/mL, about 1.55 ng/mL, about 1.6ng/mL, about 1.65 ng/mL, about 1.7 ng/mL, about 1.75 ng/mL, about 1.8ng/mL, about 1.85 ng/mL, about 1.9 ng/mL, about 1.95 ng/mL, about 2ng/mL, about 2.05 ng/mL, about 2.1 ng/mL, about 2.15 ng/mL, about 2.2ng/mL, about 2.25 ng/mL, about 2.3 ng/mL, about 2.35 ng/mL, about 2.4ng/mL, about 2.45 ng/mL, about 2.5 ng/mL, about 2.55 ng/mL, about 2.6ng/mL, about 2.65 ng/mL, about 2.7 ng/mL, about 2.75 ng/mL, about 2.8ng/mL, about 2.85 ng/mL, about 2.9 ng/mL, about 2.95 ng/mL, about 3ng/mL, about 3.1 ng/mL, about 3.2 ng/mL, about 3.3 ng/mL, about 3.4ng/mL, about 3.5 ng/mL, about 3.6 ng/mL, about 3.7 ng/mL, about 3.8ng/mL, about 3.9 ng/mL, about 4 ng/mL, about 4.1 ng/mL, about 4.2 ng/mL,about 4.3 ng/mL, about 4.4 ng/mL, about 4.5 ng/mL, about 4.6 ng/mL,about 4.7 ng/mL, about 4.8 ng/mL, about 4.9 ng/mL, about 5 ng/mL, about5.5 ng/mL, about 6 ng/mL, about 6.5 ng/mL, about 7 ng/mL, about 7.5ng/mL, about 8 ng/mL, about 8.5 ng/mL, about 9 ng/mL, about 9.5 ng/mL,about 10 ng/mL, about 11 ng/mL, about 12 ng/mL, about 13 ng/mL, about 14ng/mL, about 15 ng/mL, about 16 ng/mL, about 17 ng/mL, about 18 ng/mL,about 19 ng/mL, about 20 ng/mL, about 25 ng/mL, about 30 ng/mL, about 35ng/mL, about 40 ng/mL, about 45 ng/mL, about 50 ng/mL, about 60 ng/mL,about 70 ng/mL, about 80 ng/mL, about 90 ng/mL, or about 100 ng/mL permg of β-lactam compound administered daily, or any range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 0.5 ng/mL, about 0.55 ng/mL, about0.6 ng/mL, about 0.65 ng/mL, about 0.7 ng/mL, about 0.75 ng/mL, about0.8 ng/mL, about 0.85 ng/mL, about 0.9 ng/mL, about 0.95 ng/mL, about 1ng/mL, about 1.05 ng/mL, about 1.1 ng/mL, about 1.15 ng/mL, about 1.2ng/mL, about 1.25 ng/mL, about 1.3 ng/mL, about 1.35 ng/mL, about 1.4ng/mL, about 1.45 ng/mL, about 1.5 ng/mL, about 1.55 ng/mL, about 1.6ng/mL, about 1.65 ng/mL, about 1.7 ng/mL, about 1.75 ng/mL, about 1.8ng/mL, about 1.85 ng/mL, about 1.9 ng/mL, about 1.95 ng/mL, about 2ng/mL, about 2.05 ng/mL, about 2.1 ng/mL, about 2.15 ng/mL, about 2.2ng/mL, about 2.25 ng/mL, about 2.3 ng/mL, about 2.35 ng/mL, about 2.4ng/mL, about 2.45 ng/mL, about 2.5 ng/mL, about 2.55 ng/mL, about 2.6ng/mL, about 2.65 ng/mL, about 2.7 ng/mL, about 2.75 ng/mL, about 2.8ng/mL, about 2.85 ng/mL, about 2.9 ng/mL, about 2.95 ng/mL, about 3ng/mL, about 3.1 ng/mL, about 3.2 ng/mL, about 3.3 ng/mL, about 3.4ng/mL, about 3.5 ng/mL, about 3.6 ng/mL, about 3.7 ng/mL, about 3.8ng/mL, about 3.9 ng/mL, about 4 ng/mL, about 4.1 ng/mL, about 4.2 ng/mL,about 4.3 ng/mL, about 4.4 ng/mL, about 4.5 ng/mL, about 4.6 ng/mL,about 4.7 ng/mL, about 4.8 ng/mL, about 4.9 ng/mL, about 5 ng/mL, about5.5 ng/mL, about 6 ng/mL, about 6.5 ng/mL, about 7 ng/mL, about 7.5ng/mL, about 8 ng/mL, about 8.5 ng/mL, about 9 ng/mL, about 9.5 ng/mL,about 10 ng/mL, about 11 ng/mL, about 12 ng/mL, about 13 ng/mL, about 14ng/mL, about 15 ng/mL, about 16 ng/mL, about 17 ng/mL, about 18 ng/mL,about 19 ng/mL, about 20 ng/mL, about 25 ng/mL, about 30 ng/mL, about 35ng/mL, about 40 ng/mL, about 45 ng/mL, about 50 ng/mL, about 60 ng/mL,about 70 ng/mL, about 80 ng/mL, about 90 ng/mL, or about 100 ng/mL permg of β-lactam compound administered daily, or any range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration is at about 0.5 ng/mL, about 0.55 ng/mL, about0.6 ng/mL, about 0.65 ng/mL, about 0.7 ng/mL, about 0.75 ng/mL, about0.8 ng/mL, about 0.85 ng/mL, about 0.9 ng/mL, about 0.95 ng/mL, about 1ng/mL, about 1.05 ng/mL, about 1.1 ng/mL, about 1.15 ng/mL, about 1.2ng/mL, about 1.25 ng/mL, about 1.3 ng/mL, about 1.35 ng/mL, about 1.4ng/mL, about 1.45 ng/mL, about 1.5 ng/mL, about 1.55 ng/mL, about 1.6ng/mL, about 1.65 ng/mL, about 1.7 ng/mL, about 1.75 ng/mL, about 1.8ng/mL, about 1.85 ng/mL, about 1.9 ng/mL, about 1.95 ng/mL, about 2ng/mL, about 2.05 ng/mL, about 2.1 ng/mL, about 2.15 ng/mL, about 2.2ng/mL, about 2.25 ng/mL, about 2.3 ng/mL, about 2.35 ng/mL, about 2.4ng/mL, about 2.45 ng/mL, about 2.5 ng/mL, about 2.55 ng/mL, about 2.6ng/mL, about 2.65 ng/mL, about 2.7 ng/mL, about 2.75 ng/mL, about 2.8ng/mL, about 2.85 ng/mL, about 2.9 ng/mL, about 2.95 ng/mL, about 3ng/mL, about 3.1 ng/mL, about 3.2 ng/mL, about 3.3 ng/mL, about 3.4ng/mL, about 3.5 ng/mL, about 3.6 ng/mL, about 3.7 ng/mL, about 3.8ng/mL, about 3.9 ng/mL, about 4 ng/mL, about 4.1 ng/mL, about 4.2 ng/mL,about 4.3 ng/mL, about 4.4 ng/mL, about 4.5 ng/mL, about 4.6 ng/mL,about 4.7 ng/mL, about 4.8 ng/mL, about 4.9 ng/mL, about 5 ng/mL, about5.5 ng/mL, about 6 ng/mL, about 6.5 ng/mL, about 7 ng/mL, about 7.5ng/mL, about 8 ng/mL, about 8.5 ng/mL, about 9 ng/mL, about 9.5 ng/mL,about 10 ng/mL, about 11 ng/mL, about 12 ng/mL, about 13 ng/mL, about 14ng/mL, about 15 ng/mL, about 16 ng/mL, about 17 ng/mL, about 18 ng/mL,about 19 ng/mL, about 20 ng/mL, about 25 ng/mL, about 30 ng/mL, about 35ng/mL, about 40 ng/mL, about 45 ng/mL, about 50 ng/mL, about 60 ng/mL,about 70 ng/mL, about 80 ng/mL, about 90 ng/mL, or about 100 ng/mL permg of β-lactam compound administered daily, or any range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 0.5 hr·ng/mL, about 0.55 hr·ng/mL, about 0.6hr·ng/mL, about 0.65 hr·ng/mL, about 0.7 hr·ng/mL, about 0.75 hr·ng/mL,about 0.8 hr·ng/mL, about 0.85 hr·ng/mL, about 0.9 hr·ng/mL, about 0.95hr·ng/mL, about 1 hr·ng/mL, about 1.05 hr·ng/mL, about 1.1 hr·ng/mL,about 1.15 hr·ng/mL, about 1.2 hr·ng/mL, about 1.25 hr·ng/mL, about 1.3hr·ng/mL, about 1.35 hr·ng/mL, about 1.4 hr·ng/mL, about 1.45 hr·ng/mL,about 1.5 hr·ng/mL, about 1.55 hr·ng/mL, about 1.6 hr·ng/mL, about 1.65hr·ng/mL, about 1.7 hr·ng/mL, about 1.75 hr·ng/mL, about 1.8 hr·ng/mL,about 1.85 hr·ng/mL, about 1.9 hr·ng/mL, about 1.95 hr·ng/mL, about 2hr·ng/mL, about 2.05 hr·ng/mL, about 2.1 hr·ng/mL, about 2.15 hr·ng/mL,about 2.2 hr·ng/mL, about 2.25 hr·ng/mL, about 2.3 hr·ng/mL, about 2.35hr·ng/mL, about 2.4 hr·ng/mL, about 2.45 hr·ng/mL, about 2.5 hr·ng/mL,about 2.55 hr·ng/mL, about 2.6 hr·ng/mL, about 2.65 hr·ng/mL, about 2.7hr·ng/mL, about 2.75 hr·ng/mL, about 2.8 hr·ng/mL, about 2.85 hr·ng/mL,about 2.9 hr·ng/mL, about 2.95 hr·ng/mL, about 3 hr·ng/mL, about 3.1hr·ng/mL, about 3.2 hr·ng/mL, about 3.3 hr·ng/mL, about 3.4 hr·ng/mL,about 3.5 hr·ng/mL, about 3.6 hr·ng/mL, about 3.7 hr·ng/mL, about 3.8hr·ng/mL, about 3.9 hr·ng/mL, about 4 hr·ng/mL, about 4.1 hr·ng/mL,about 4.2 hr·ng/mL, about 4.3 hr·ng/mL, about 4.4 hr·ng/mL, about 4.5hr·ng/mL, about 4.6 hr·ng/mL, about 4.7 hr·ng/mL, about 4.8 hr·ng/mL,about 4.9 hr·ng/mL, about 5 hr·ng/mL, about 5.5 hr·ng/mL, about 6hr·ng/mL, about 6.5 hr·ng/mL, about 7 hr·ng/mL, about 7.5 hr·ng/mL,about 8 hr·ng/mL, about 8.5 hr·ng/mL, about 9 hr·ng/mL, about 9.5hr·ng/mL, about 10 hr·ng/mL, about 11 hr·ng/mL, about 12 hr·ng/mL, about13 hr·ng/mL, about 14 hr·ng/mL, about 15 hr·ng/mL, about 16 hr·ng/mL,about 17 hr·ng/mL, about 18 hr·ng/mL, about 19 hr·ng/mL, about 20hr·ng/mL, about 25 hr·ng/mL, about 30 hr·ng/mL, about 35 hr·ng/mL, about40 hr·ng/mL, about 45 hr·ng/mL, about 50 hr·ng/mL, about 60 hr·ng/mL,about 70 hr·ng/mL, about 80 hr·ng/mL, about 90 hr·ng/mL, or about 100hr·ng/mL per mg of β-lactam compound administered daily, or any rangetherebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 0.5 hr·ng/mL, about 0.55 hr·ng/mL, about0.6 hr·ng/mL, about 0.65 hr·ng/mL, about 0.7 hr·ng/mL, about 0.75hr·ng/mL, about 0.8 hr·ng/mL, about 0.85 hr·ng/mL, about 0.9 hr·ng/mL,about 0.95 hr·ng/mL, about 1 hr·ng/mL, about 1.05 hr·ng/mL, about 1.1hr·ng/mL, about 1.15 hr·ng/mL, about 1.2 hr·ng/mL, about 1.25 hr·ng/mL,about 1.3 hr·ng/mL, about 1.35 hr·ng/mL, about 1.4 hr·ng/mL, about 1.45hr·ng/mL, about 1.5 hr·ng/mL, about 1.55 hr·ng/mL, about 1.6 hr·ng/mL,about 1.65 hr·ng/mL, about 1.7 hr·ng/mL, about 1.75 hr·ng/mL, about 1.8hr·ng/mL, about 1.85 hr·ng/mL, about 1.9 hr·ng/mL, about 1.95 hr·ng/mL,about 2 hr·ng/mL, about 2.05 hr·ng/mL, about 2.1 hr·ng/mL, about 2.15hr·ng/mL, about 2.2 hr·ng/mL, about 2.25 hr·ng/mL, about 2.3 hr·ng/mL,about 2.35 hr·ng/mL, about 2.4 hr·ng/mL, about 2.45 hr·ng/mL, about 2.5hr·ng/mL, about 2.55 hr·ng/mL, about 2.6 hr·ng/mL, about 2.65 hr·ng/mL,about 2.7 hr·ng/mL, about 2.75 hr·ng/mL, about 2.8 hr·ng/mL, about 2.85hr·ng/mL, about 2.9 hr·ng/mL, about 2.95 hr·ng/mL, about 3 hr·ng/mL,about 3.1 hr·ng/mL, about 3.2 hr·ng/mL, about 3.3 hr·ng/mL, about 3.4hr·ng/mL, about 3.5 hr·ng/mL, about 3.6 hr·ng/mL, about 3.7 hr·ng/mL,about 3.8 hr·ng/mL, about 3.9 hr·ng/mL, about 4 hr·ng/mL, about 4.1hr·ng/mL, about 4.2 hr·ng/mL, about 4.3 hr·ng/mL, about 4.4 hr·ng/mL,about 4.5 hr·ng/mL, about 4.6 hr·ng/mL, about 4.7 hr·ng/mL, about 4.8hr·ng/mL, about 4.9 hr·ng/mL, about 5 hr·ng/mL, about 5.5 hr·ng/mL,about 6 hr·ng/mL, about 6.5 hr·ng/mL, about 7 hr·ng/mL, about 7.5hr·ng/mL, about 8 hr·ng/mL, about 8.5 hr·ng/mL, about 9 hr·ng/mL, about9.5 hr·ng/mL, about 10 hr·ng/mL, about 11 hr·ng/mL, about 12 hr·ng/mL,about 13 hr·ng/mL, about 14 hr·ng/mL, about 15 hr·ng/mL, about 16hr·ng/mL, about 17 hr·ng/mL, about 18 hr·ng/mL, about 19 hr·ng/mL, about20 hr·ng/mL, about 25 hr·ng/mL, about 30 hr·ng/mL, about 35 hr·ng/mL,about 40 hr·ng/mL, about 45 hr·ng/mL, about 50 hr·ng/mL, about 60hr·ng/mL, about 70 hr·ng/mL, about 80 hr·ng/mL, about 90 hr·ng/mL, orabout 100 hr·ng/mL per mg of β-lactam compound administered daily, orany range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 0.5 hr·ng/mL, about 0.55 hr·ng/mL, about0.6 hr·ng/mL, about 0.65 hr·ng/mL, about 0.7 hr·ng/mL, about 0.75hr·ng/mL, about 0.8 hr·ng/mL, about 0.85 hr·ng/mL, about 0.9 hr·ng/mL,about 0.95 hr·ng/mL, about 1 hr·ng/mL, about 1.05 hr·ng/mL, about 1.1hr·ng/mL, about 1.15 hr·ng/mL, about 1.2 hr·ng/mL, about 1.25 hr·ng/mL,about 1.3 hr·ng/mL, about 1.35 hr·ng/mL, about 1.4 hr·ng/mL, about 1.45hr·ng/mL, about 1.5 hr·ng/mL, about 1.55 hr·ng/mL, about 1.6 hr·ng/mL,about 1.65 hr·ng/mL, about 1.7 hr·ng/mL, about 1.75 hr·ng/mL, about 1.8hr·ng/mL, about 1.85 hr·ng/mL, about 1.9 hr·ng/mL, about 1.95 hr·ng/mL,about 2 hr·ng/mL, about 2.05 hr·ng/mL, about 2.1 hr·ng/mL, about 2.15hr·ng/mL, about 2.2 hr·ng/mL, about 2.25 hr·ng/mL, about 2.3 hr·ng/mL,about 2.35 hr·ng/mL, about 2.4 hr·ng/mL, about 2.45 hr·ng/mL, about 2.5hr·ng/mL, about 2.55 hr·ng/mL, about 2.6 hr·ng/mL, about 2.65 hr·ng/mL,about 2.7 hr·ng/mL, about 2.75 hr·ng/mL, about 2.8 hr·ng/mL, about 2.85hr·ng/mL, about 2.9 hr·ng/mL, about 2.95 hr·ng/mL, about 3 hr·ng/mL,about 3.1 hr·ng/mL, about 3.2 hr·ng/mL, about 3.3 hr·ng/mL, about 3.4hr·ng/mL, about 3.5 hr·ng/mL, about 3.6 hr·ng/mL, about 3.7 hr·ng/mL,about 3.8 hr·ng/mL, about 3.9 hr·ng/mL, about 4 hr·ng/mL, about 4.1hr·ng/mL, about 4.2 hr·ng/mL, about 4.3 hr·ng/mL, about 4.4 hr·ng/mL,about 4.5 hr·ng/mL, about 4.6 hr·ng/mL, about 4.7 hr·ng/mL, about 4.8hr·ng/mL, about 4.9 hr·ng/mL, about 5 hr·ng/mL, about 5.5 hr·ng/mL,about 6 hr·ng/mL, about 6.5 hr·ng/mL, about 7 hr·ng/mL, about 7.5hr·ng/mL, about 8 hr·ng/mL, about 8.5 hr·ng/mL, about 9 hr·ng/mL, about9.5 hr·ng/mL, about 10 hr·ng/mL, about 11 hr·ng/mL, about 12 hr·ng/mL,about 13 hr·ng/mL, about 14 hr·ng/mL, about 15 hr·ng/mL, about 16hr·ng/mL, about 17 hr·ng/mL, about 18 hr·ng/mL, about 19 hr·ng/mL, about20 hr·ng/mL, about 25 hr·ng/mL, about 30 hr·ng/mL, about 35 hr·ng/mL,about 40 hr·ng/mL, about 45 hr·ng/mL, about 50 hr·ng/mL, about 60hr·ng/mL, about 70 hr·ng/mL, about 80 hr·ng/mL, about 90 hr·ng/mL, orabout 100 hr·ng/mL per mg of β-lactam compound administered daily, orany range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 0.5 hr·ng/mL, about 0.55 hr·ng/mL,about 0.6 hr·ng/mL, about 0.65 hr·ng/mL, about 0.7 hr·ng/mL, about 0.75hr·ng/mL, about 0.8 hr·ng/mL, about 0.85 hr·ng/mL, about 0.9 hr·ng/mL,about 0.95 hr·ng/mL, about 1 hr·ng/mL, about 1.05 hr·ng/mL, about 1.1hr·ng/mL, about 1.15 hr·ng/mL, about 1.2 hr·ng/mL, about 1.25 hr·ng/mL,about 1.3 hr·ng/mL, about 1.35 hr·ng/mL, about 1.4 hr·ng/mL, about 1.45hr·ng/mL, about 1.5 hr·ng/mL, about 1.55 hr·ng/mL, about 1.6 hr·ng/mL,about 1.65 hr·ng/mL, about 1.7 hr·ng/mL, about 1.75 hr·ng/mL, about 1.8hr·ng/mL, about 1.85 hr·ng/mL, about 1.9 hr·ng/mL, about 1.95 hr·ng/mL,about 2 hr·ng/mL, about 2.05 hr·ng/mL, about 2.1 hr·ng/mL, about 2.15hr·ng/mL, about 2.2 hr·ng/mL, about 2.25 hr·ng/mL, about 2.3 hr·ng/mL,about 2.35 hr·ng/mL, about 2.4 hr·ng/mL, about 2.45 hr·ng/mL, about 2.5hr·ng/mL, about 2.55 hr·ng/mL, about 2.6 hr·ng/mL, about 2.65 hr·ng/mL,about 2.7 hr·ng/mL, about 2.75 hr·ng/mL, about 2.8 hr·ng/mL, about 2.85hr·ng/mL, about 2.9 hr·ng/mL, about 2.95 hr·ng/mL, about 3 hr·ng/mL,about 3.1 hr·ng/mL, about 3.2 hr·ng/mL, about 3.3 hr·ng/mL, about 3.4hr·ng/mL, about 3.5 hr·ng/mL, about 3.6 hr·ng/mL, about 3.7 hr·ng/mL,about 3.8 hr·ng/mL, about 3.9 hr·ng/mL, about 4 hr·ng/mL, about 4.1hr·ng/mL, about 4.2 hr·ng/mL, about 4.3 hr·ng/mL, about 4.4 hr·ng/mL,about 4.5 hr·ng/mL, about 4.6 hr·ng/mL, about 4.7 hr·ng/mL, about 4.8hr·ng/mL, about 4.9 hr·ng/mL, about 5 hr·ng/mL, about 5.5 hr·ng/mL,about 6 hr·ng/mL, about 6.5 hr·ng/mL, about 7 hr·ng/mL, about 7.5hr·ng/mL, about 8 hr·ng/mL, about 8.5 hr·ng/mL, about 9 hr·ng/mL, about9.5 hr·ng/mL, about 10 hr·ng/mL, about 11 hr·ng/mL, about 12 hr·ng/mL,about 13 hr·ng/mL, about 14 hr·ng/mL, about 15 hr·ng/mL, about 16hr·ng/mL, about 17 hr·ng/mL, about 18 hr·ng/mL, about 19 hr·ng/mL, about20 hr·ng/mL, about 25 hr·ng/mL, about 30 hr·ng/mL, about 35 hr·ng/mL,about 40 hr·ng/mL, about 45 hr·ng/mL, about 50 hr·ng/mL, about 60hr·ng/mL, about 70 hr·ng/mL, about 80 hr·ng/mL, about 90 hr·ng/mL, orabout 100 hr·ng/mL per mg of β-lactam compound administered daily, orany range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration ranges from about 1500 ng/mL to about 2500 ng/mL,from about 1600 ng/mL to about 2400 ng/mL, from about 1700 ng/mL toabout 2300 ng/mL, from about 1800 ng/mL to about 2200 ng/mL, from about1900 ng/mL to about 2100 ng/mL, from about 1950 ng/mL to about 2050ng/mL, from about 1980 ng/mL to about 2020 ng/mL, from about 1990 ng/mLto about 2010 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration is at about 2000 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration ranges from about 700 ng/mL to about 1800 ng/mL,from about 800 ng/mL to about 1700 ng/mL, from about 900 ng/mL to about1600 ng/mL, from about 1000 ng/mL to about 1500 ng/mL, from about 1100ng/mL to about 1400 ng/mL, from about 1200 ng/mL to about 1300 ng/mL,from about 1230 ng/mL to about 1270 ng/mL, from about 1240 ng/mL toabout 1260 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration is at about 1250 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration ranges from about 1600 ng/mL to about 2700ng/mL, from about 1700 ng/mL to about 2600 ng/mL, from about 1800 ng/mLto about 2500 ng/mL, from about 1900 ng/mL to about 2400 ng/mL, fromabout 2000 ng/mL to about 2300 ng/mL, from about 2100 ng/mL to about2200 ng/mL, from about 2130 ng/mL to about 2170 ng/mL, from about 2140ng/mL to about 2160 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 2150 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration ranges from about 1600 ng/mL to about 2700ng/mL, from about 1700 ng/mL to about 2600 ng/mL, from about 1800 ng/mLto about 2500 ng/mL, from about 1900 ng/mL to about 2400 ng/mL, fromabout 2000 ng/mL to about 2300 ng/mL, from about 2050 ng/mL to about2200 ng/mL, from about 2100 ng/mL to about 2140 ng/mL, from about 2110ng/mL to about 2130 ng/mL.

In some embodiments, the resulted Cm, of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 2120 ng/mL.

In some embodiments, the resulted Cm, of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration ranges from about 1200 ng/mL to about 2200 ng/mL, fromabout 1300 ng/mL to about 2100 ng/mL, from about 1400 ng/mL to about2000 ng/mL, from about 1500 ng/mL to about 1900 ng/mL, from about 1600ng/mL to about 1800 ng/mL, from about 1650 ng/mL to about 1750 ng/mL,from about 1680 ng/mL to about 1720 ng/mL, from about 1690 ng/mL toabout 1710 ng/mL.

In some embodiments, the resulted Cm, of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 1700 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration ranges from about 800 ng/mL to about 1800 ng/mL,from about 900 ng/mL to about 1700 ng/mL, from about 1000 ng/mL to about1600 ng/mL, from about 1100 ng/mL to about 1500 ng/mL, from about 1200ng/mL to about 1400 ng/mL, from about 1250 ng/mL to about 1350 ng/mL,from about 1270 ng/mL to about 1310 ng/mL, from about 1280 ng/mL toabout 1300 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the seventh dayof the administration is at about 1290 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration ranges from about 1200 ng/mL to about 2200ng/mL, from about 1300 ng/mL to about 2100 ng/mL, from about 1400 ng/mLto about 2000 ng/mL, from about 1500 ng/mL to about 1900 ng/mL, fromabout 1600 ng/mL to about 1850 ng/mL, from about 1650 ng/mL to about1800 ng/mL, from about 1700 ng/mL to about 1740 ng/mL, from about 1710ng/mL to about 1730 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 1720 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration ranges from about 900 ng/mL to about 2000ng/mL, from about 1000 ng/mL to about 1900 ng/mL, from about 1100 ng/mLto about 1800 ng/mL, from about 1200 ng/mL to about 1700 ng/mL, fromabout 1300 ng/mL to about 1600 ng/mL, from about 1400 ng/mL to about1550 ng/mL, from about 1460 ng/mL to about 1500 ng/mL, from about 1470ng/mL to about 1490 ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration is at about 1480 ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration ranges from about 2500 hr·ng/mL to about 3200 hr·ng/mL,from about 2600 hr·ng/mL to about 3100 hr·ng/mL, from about 2700hr·ng/mL to about 3000 hr·ng/mL, from about 2750 hr·ng/mL to about 2950hr·ng/mL, from about 2800 hr·ng/mL to about 2870 hr·ng/mL, ranges fromabout 2810 hr·ng/mL to about 2860 hr·ng/mL, or from about 2820 hr·ng/mLto about 2850 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 2840 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration ranges from about 1600 hr·ng/mL to about 2200hr·ng/mL, from about 1700 hr·ng/mL to about 2100 hr·ng/mL, from about1800 hr·ng/mL to about 2000 hr·ng/mL, from about 1850 hr·ng/mL to about1950 hr·ng/mL, from about 1860 hr·ng/mL to about 1920 hr·ng/mL, rangesfrom about 1870 hr·ng/mL to about 1910 hr·ng/mL, or from about 1880hr·ng/mL to about 1900 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 1890 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration ranges from about 3900 hr·ng/mL to about 4500hr·ng/mL, from about 4000 hr·ng/mL to about 4400 hr·ng/mL, from about4100 hr·ng/mL to about 4300 hr·ng/mL, from about 4150 hr·ng/mL to about4250 hr·ng/mL, from about 4160 hr·ng/mL to about 4220 hr·ng/mL, rangesfrom about 4170 hr·ng/mL to about 4210 hr·ng/mL, or from about 4180hr·ng/mL to about 4200 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 4190 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration ranges from about 4100 hr·ng/mL to about 4700hr·ng/mL, from about 4200 hr·ng/mL to about 4600 hr·ng/mL, from about4300 hr·ng/mL to about 4500 hr·ng/mL, from about 4350 hr·ng/mL to about4450 hr·ng/mL, from about 4370 hr·ng/mL to about 4430 hr·ng/mL, rangesfrom about 4380 hr·ng/mL to about 4420 hr·ng/mL, or from about 4390hr·ng/mL to about 4410 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 4400 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration ranges from about 3200 hr·ng/mL to about 4000 hr·ng/mL,from about 3300 hr·ng/mL to about 3900 hr·ng/mL, from about 3400hr·ng/mL to about 3800 hr·ng/mL, from about 3500 hr·ng/mL to about 3700hr·ng/mL, from about 3590 hr·ng/mL to about 3650 hr·ng/mL, ranges fromabout 3600 hr·ng/mL to about 3640 hr·ng/mL, or from about 3610 hr·ng/mLto about 3630 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 3620 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration ranges from about 2200 hr·ng/mL to about 3100hr·ng/mL, from about 2300 hr·ng/mL to about 3000 hr·ng/mL, from about2400 hr·ng/mL to about 2900 hr·ng/mL, from about 2500 hr·ng/mL to about2800 hr·ng/mL, from about 2600 hr·ng/mL to about 2700 hr·ng/mL, rangesfrom about 2610 hr·ng/mL to about 2650 hr·ng/mL, or from about 2620hr·ng/mL to about 2640 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 2630 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration ranges from about 3400 hr·ng/mL to about 4300hr·ng/mL, from about 3500 hr·ng/mL to about 4200 hr·ng/mL, from about3600 hr·ng/mL to about 4100 hr·ng/mL, from about 3700 hr·ng/mL to about4000 hr·ng/mL, from about 3800 hr·ng/mL to about 3900 hr·ng/mL, rangesfrom about 3840 hr·ng/mL to about 3880 hr·ng/mL, or from about 3850hr·ng/mL to about 3870 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 3860 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration ranges from about 3900 hr·ng/mL to about 4700hr·ng/mL, from about 4000 hr·ng/mL to about 4600 hr·ng/mL, from about4100 hr·ng/mL to about 4400 hr·ng/mL, from about 4200 hr·ng/mL to about4400 hr·ng/mL, from about 4250 hr·ng/mL to about 4350 hr·ng/mL, rangesfrom about 4260 hr·ng/mL to about 4300 hr·ng/mL, or from about 4270hr·ng/mL to about 4290 hr·ng/mL.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 4280 hr·ng/mL.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the comparable subject at the first day ofthe administration is at about 100 ng/mL, about 150 ng/mL, about 200ng/mL, about 250 ng/mL, about 300 ng/mL, about 350 ng/mL, about 400ng/mL, about 450 ng/mL, about 500 ng/mL, about 550 ng/mL, about 600ng/mL, about 650 ng/mL, about 700 ng/mL, about 750 ng/mL, about 800ng/mL, about 850 ng/mL, about 900 ng/mL, about 950 ng/mL, about 1000ng/mL, about 1050 ng/mL, about 1100 ng/mL, about 1150 ng/mL, about 1200ng/mL, about 1250 ng/mL, about 1300 ng/mL, about 1350 ng/mL, about 1400ng/mL, about 1450 ng/mL, about 1500 ng/mL, about 1550 ng/mL, about 1600ng/mL, about 1650 ng/mL, about 1700 ng/mL, about 1750 ng/mL, about 1800ng/mL, about 1850 ng/mL, about 1900 ng/mL, about 1950 ng/mL, about 2000ng/mL, about 2050 ng/mL, about 2100 ng/mL, about 2150 ng/mL, about 2200ng/mL, about 2250 ng/mL, about 2300 ng/mL, about 2350 ng/mL, about 2400ng/mL, about 2450 ng/mL, about 2500 ng/mL, about 2550 ng/mL, about 2600ng/mL, about 2650 ng/mL, about 2700 ng/mL, about 2750 ng/mL, about 2800ng/mL, about 2850 ng/mL, about 2900 ng/mL, about 2950 ng/mL, about 3000ng/mL, about 3050 ng/mL, about 3100 ng/mL, about 3150 ng/mL, about 3200ng/mL, about 3250 ng/mL, about 3300 ng/mL, about 3350 ng/mL, about 3400ng/mL, about 3450 ng/mL, about 3500 ng/mL, about 3550 ng/mL, about 3600ng/mL, about 3650 ng/mL, about 3700 ng/mL, about 3750 ng/mL, about 3800ng/mL, about 3850 ng/mL, about 3900 ng/mL, about 3950 ng/mL, about 4000ng/mL, about 4050 ng/mL, about 4100 ng/mL, about 4150 ng/mL, about 4200ng/mL, about 4250 ng/mL, about 4300 ng/mL, about 4350 ng/mL, about 4400ng/mL, about 4450 ng/mL, about 4500 ng/mL, about 4550 ng/mL, about 4600ng/mL, about 4650 ng/mL, about 4700 ng/mL, about 4750 ng/mL, about 4800ng/mL, about 4850 ng/mL, about 4900 ng/mL, about 4950 ng/mL, about 5000ng/mL, about 5100 ng/mL, about 5200 ng/mL, about 5300 ng/mL, about 5400ng/mL, about 5500 ng/mL, about 5600 ng/mL, about 5700 ng/mL, about 5800ng/mL, about 5900 ng/mL, about 6000 ng/mL, about 6500 ng/mL, about 7000ng/mL, about 7500 ng/mL, about 8000 ng/mL, about 8500 ng/mL, about 9000ng/mL, about 9500 ng/mL, about 10000 ng/mL, about 11000 ng/mL, about12000 ng/mL, about 13000 ng/mL, about 14000 ng/mL, about 15000 ng/mL,about 16000 ng/mL, about 17000 ng/mL, about 18000 ng/mL, about 19000ng/mL, or about 20000 ng/mL, or any range therebetween.

In some embodiments, the resulted Cm. of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 100 ng/mL, about 150 ng/mL, about 200ng/mL, about 250 ng/mL, about 300 ng/mL, about 350 ng/mL, about 400ng/mL, about 450 ng/mL, about 500 ng/mL, about 550 ng/mL, about 600ng/mL, about 650 ng/mL, about 700 ng/mL, about 750 ng/mL, about 800ng/mL, about 850 ng/mL, about 900 ng/mL, about 950 ng/mL, about 1000ng/mL, about 1050 ng/mL, about 1100 ng/mL, about 1150 ng/mL, about 1200ng/mL, about 1250 ng/mL, about 1300 ng/mL, about 1350 ng/mL, about 1400ng/mL, about 1450 ng/mL, about 1500 ng/mL, about 1550 ng/mL, about 1600ng/mL, about 1650 ng/mL, about 1700 ng/mL, about 1750 ng/mL, about 1800ng/mL, about 1850 ng/mL, about 1900 ng/mL, about 1950 ng/mL, about 2000ng/mL, about 2050 ng/mL, about 2100 ng/mL, about 2150 ng/mL, about 2200ng/mL, about 2250 ng/mL, about 2300 ng/mL, about 2350 ng/mL, about 2400ng/mL, about 2450 ng/mL, about 2500 ng/mL, about 2550 ng/mL, about 2600ng/mL, about 2650 ng/mL, about 2700 ng/mL, about 2750 ng/mL, about 2800ng/mL, about 2850 ng/mL, about 2900 ng/mL, about 2950 ng/mL, about 3000ng/mL, about 3050 ng/mL, about 3100 ng/mL, about 3150 ng/mL, about 3200ng/mL, about 3250 ng/mL, about 3300 ng/mL, about 3350 ng/mL, about 3400ng/mL, about 3450 ng/mL, about 3500 ng/mL, about 3550 ng/mL, about 3600ng/mL, about 3650 ng/mL, about 3700 ng/mL, about 3750 ng/mL, about 3800ng/mL, about 3850 ng/mL, about 3900 ng/mL, about 3950 ng/mL, about 4000ng/mL, about 4050 ng/mL, about 4100 ng/mL, about 4150 ng/mL, about 4200ng/mL, about 4250 ng/mL, about 4300 ng/mL, about 4350 ng/mL, about 4400ng/mL, about 4450 ng/mL, about 4500 ng/mL, about 4550 ng/mL, about 4600ng/mL, about 4650 ng/mL, about 4700 ng/mL, about 4750 ng/mL, about 4800ng/mL, about 4850 ng/mL, about 4900 ng/mL, about 4950 ng/mL, about 5000ng/mL, about 5100 ng/mL, about 5200 ng/mL, about 5300 ng/mL, about 5400ng/mL, about 5500 ng/mL, about 5600 ng/mL, about 5700 ng/mL, about 5800ng/mL, about 5900 ng/mL, about 6000 ng/mL, about 6500 ng/mL, about 7000ng/mL, about 7500 ng/mL, about 8000 ng/mL, about 8500 ng/mL, about 9000ng/mL, about 9500 ng/mL, about 10000 ng/mL, about 11000 ng/mL, about12000 ng/mL, about 13000 ng/mL, about 14000 ng/mL, about 15000 ng/mL,about 16000 ng/mL, about 17000 ng/mL, about 18000 ng/mL, about 19000ng/mL, or about 20000 ng/mL, or any range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the firstday of the administration is at about 100 ng/mL, about 150 ng/mL, about200 ng/mL, about 250 ng/mL, about 300 ng/mL, about 350 ng/mL, about 400ng/mL, about 450 ng/mL, about 500 ng/mL, about 550 ng/mL, about 600ng/mL, about 650 ng/mL, about 700 ng/mL, about 750 ng/mL, about 800ng/mL, about 850 ng/mL, about 900 ng/mL, about 950 ng/mL, about 1000ng/mL, about 1050 ng/mL, about 1100 ng/mL, about 1150 ng/mL, about 1200ng/mL, about 1250 ng/mL, about 1300 ng/mL, about 1350 ng/mL, about 1400ng/mL, about 1450 ng/mL, about 1500 ng/mL, about 1550 ng/mL, about 1600ng/mL, about 1650 ng/mL, about 1700 ng/mL, about 1750 ng/mL, about 1800ng/mL, about 1850 ng/mL, about 1900 ng/mL, about 1950 ng/mL, about 2000ng/mL, about 2050 ng/mL, about 2100 ng/mL, about 2150 ng/mL, about 2200ng/mL, about 2250 ng/mL, about 2300 ng/mL, about 2350 ng/mL, about 2400ng/mL, about 2450 ng/mL, about 2500 ng/mL, about 2550 ng/mL, about 2600ng/mL, about 2650 ng/mL, about 2700 ng/mL, about 2750 ng/mL, about 2800ng/mL, about 2850 ng/mL, about 2900 ng/mL, about 2950 ng/mL, about 3000ng/mL, about 3050 ng/mL, about 3100 ng/mL, about 3150 ng/mL, about 3200ng/mL, about 3250 ng/mL, about 3300 ng/mL, about 3350 ng/mL, about 3400ng/mL, about 3450 ng/mL, about 3500 ng/mL, about 3550 ng/mL, about 3600ng/mL, about 3650 ng/mL, about 3700 ng/mL, about 3750 ng/mL, about 3800ng/mL, about 3850 ng/mL, about 3900 ng/mL, about 3950 ng/mL, about 4000ng/mL, about 4050 ng/mL, about 4100 ng/mL, about 4150 ng/mL, about 4200ng/mL, about 4250 ng/mL, about 4300 ng/mL, about 4350 ng/mL, about 4400ng/mL, about 4450 ng/mL, about 4500 ng/mL, about 4550 ng/mL, about 4600ng/mL, about 4650 ng/mL, about 4700 ng/mL, about 4750 ng/mL, about 4800ng/mL, about 4850 ng/mL, about 4900 ng/mL, about 4950 ng/mL, about 5000ng/mL, about 5100 ng/mL, about 5200 ng/mL, about 5300 ng/mL, about 5400ng/mL, about 5500 ng/mL, about 5600 ng/mL, about 5700 ng/mL, about 5800ng/mL, about 5900 ng/mL, about 6000 ng/mL, about 6500 ng/mL, about 7000ng/mL, about 7500 ng/mL, about 8000 ng/mL, about 8500 ng/mL, about 9000ng/mL, about 9500 ng/mL, about 10000 ng/mL, about 11000 ng/mL, about12000 ng/mL, about 13000 ng/mL, about 14000 ng/mL, about 15000 ng/mL,about 16000 ng/mL, about 17000 ng/mL, about 18000 ng/mL, about 19000ng/mL, or about 20000 ng/mL, or any range therebetween.

In some embodiments, the resulted C_(max) of the plasma concentrationfor the β-lactam compound in the subject in need thereof at the seventhday of the administration is at about 100 ng/mL, about 150 ng/mL, about200 ng/mL, about 250 ng/mL, about 300 ng/mL, about 350 ng/mL, about 400ng/mL, about 450 ng/mL, about 500 ng/mL, about 550 ng/mL, about 600ng/mL, about 650 ng/mL, about 700 ng/mL, about 750 ng/mL, about 800ng/mL, about 850 ng/mL, about 900 ng/mL, about 950 ng/mL, about 1000ng/mL, about 1050 ng/mL, about 1100 ng/mL, about 1150 ng/mL, about 1200ng/mL, about 1250 ng/mL, about 1300 ng/mL, about 1350 ng/mL, about 1400ng/mL, about 1450 ng/mL, about 1500 ng/mL, about 1550 ng/mL, about 1600ng/mL, about 1650 ng/mL, about 1700 ng/mL, about 1750 ng/mL, about 1800ng/mL, about 1850 ng/mL, about 1900 ng/mL, about 1950 ng/mL, about 2000ng/mL, about 2050 ng/mL, about 2100 ng/mL, about 2150 ng/mL, about 2200ng/mL, about 2250 ng/mL, about 2300 ng/mL, about 2350 ng/mL, about 2400ng/mL, about 2450 ng/mL, about 2500 ng/mL, about 2550 ng/mL, about 2600ng/mL, about 2650 ng/mL, about 2700 ng/mL, about 2750 ng/mL, about 2800ng/mL, about 2850 ng/mL, about 2900 ng/mL, about 2950 ng/mL, about 3000ng/mL, about 3050 ng/mL, about 3100 ng/mL, about 3150 ng/mL, about 3200ng/mL, about 3250 ng/mL, about 3300 ng/mL, about 3350 ng/mL, about 3400ng/mL, about 3450 ng/mL, about 3500 ng/mL, about 3550 ng/mL, about 3600ng/mL, about 3650 ng/mL, about 3700 ng/mL, about 3750 ng/mL, about 3800ng/mL, about 3850 ng/mL, about 3900 ng/mL, about 3950 ng/mL, about 4000ng/mL, about 4050 ng/mL, about 4100 ng/mL, about 4150 ng/mL, about 4200ng/mL, about 4250 ng/mL, about 4300 ng/mL, about 4350 ng/mL, about 4400ng/mL, about 4450 ng/mL, about 4500 ng/mL, about 4550 ng/mL, about 4600ng/mL, about 4650 ng/mL, about 4700 ng/mL, about 4750 ng/mL, about 4800ng/mL, about 4850 ng/mL, about 4900 ng/mL, about 4950 ng/mL, about 5000ng/mL, about 5100 ng/mL, about 5200 ng/mL, about 5300 ng/mL, about 5400ng/mL, about 5500 ng/mL, about 5600 ng/mL, about 5700 ng/mL, about 5800ng/mL, about 5900 ng/mL, about 6000 ng/mL, about 6500 ng/mL, about 7000ng/mL, about 7500 ng/mL, about 8000 ng/mL, about 8500 ng/mL, about 9000ng/mL, about 9500 ng/mL, about 10000 ng/mL, about 11000 ng/mL, about12000 ng/mL, about 13000 ng/mL, about 14000 ng/mL, about 15000 ng/mL,about 16000 ng/mL, about 17000 ng/mL, about 18000 ng/mL, about 19000ng/mL, or about 20000 ng/mL, or any range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the first day of theadministration is at about 100 hr·ng/mL, about 150 hr·ng/mL, about 200hr·ng/mL, about 250 hr·ng/mL, about 300 hr·ng/mL, about 350 hr·ng/mL,about 400 hr·ng/mL, about 450 hr·ng/mL, about 500 hr·ng/mL, about 550hr·ng/mL, about 600 hr·ng/mL, about 650 hr·ng/mL, about 700 hr·ng/mL,about 750 hr·ng/mL, about 800 hr·ng/mL, about 850 hr·ng/mL, about 900hr·ng/mL, about 950 hr·ng/mL, about 1000 hr·ng/mL, about 1050 hr·ng/mL,about 1100 hr·ng/mL, about 1150 hr·ng/mL, about 1200 hr·ng/mL, about1250 hr·ng/mL, about 1300 hr·ng/mL, about 1350 hr·ng/mL, about 1400hr·ng/mL, about 1450 hr·ng/mL, about 1500 hr·ng/mL, about 1550 hr·ng/mL,about 1600 hr·ng/mL, about 1650 hr·ng/mL, about 1700 hr·ng/mL, about1750 hr·ng/mL, about 1800 hr·ng/mL, about 1850 hr·ng/mL, about 1900hr·ng/mL, about 1950 hr·ng/mL, about 2000 hr·ng/mL, about 2050 hr·ng/mL,about 2100 hr·ng/mL, about 2150 hr·ng/mL, about 2200 hr·ng/mL, about2250 hr·ng/mL, about 2300 hr·ng/mL, about 2350 hr·ng/mL, about 2400hr·ng/mL, about 2450 hr·ng/mL, about 2500 hr·ng/mL, about 2550 hr·ng/mL,about 2600 hr·ng/mL, about 2650 hr·ng/mL, about 2700 hr·ng/mL, about2750 hr·ng/mL, about 2800 hr·ng/mL, about 2850 hr·ng/mL, about 2900hr·ng/mL, about 2950 hr·ng/mL, about 3000 hr·ng/mL, about 3050 hr·ng/mL,about 3100 hr·ng/mL, about 3150 hr·ng/mL, about 3200 hr·ng/mL, about3250 hr·ng/mL, about 3300 hr·ng/mL, about 3350 hr·ng/mL, about 3400hr·ng/mL, about 3450 hr·ng/mL, about 3500 hr·ng/mL, about 3550 hr·ng/mL,about 3600 hr·ng/mL, about 3650 hr·ng/mL, about 3700 hr·ng/mL, about3750 hr·ng/mL, about 3800 hr·ng/mL, about 3850 hr·ng/mL, about 3900hr·ng/mL, about 3950 hr·ng/mL, about 4000 hr·ng/mL, about 4050 hr·ng/mL,about 4100 hr·ng/mL, about 4150 hr·ng/mL, about 4200 hr·ng/mL, about4250 hr·ng/mL, about 4300 hr·ng/mL, about 4350 hr·ng/mL, about 4400hr·ng/mL, about 4450 hr·ng/mL, about 4500 hr·ng/mL, about 4550 hr·ng/mL,about 4600 hr·ng/mL, about 4650 hr·ng/mL, about 4700 hr·ng/mL, about4750 hr·ng/mL, about 4800 hr·ng/mL, about 4850 hr·ng/mL, about 4900hr·ng/mL, about 4950 hr·ng/mL, about 5000 hr·ng/mL, about 5100 hr·ng/mL,about 5200 hr·ng/mL, about 5300 hr·ng/mL, about 5400 hr·ng/mL, about5500 hr·ng/mL, about 5600 hr·ng/mL, about 5700 hr·ng/mL, about 5800hr·ng/mL, about 5900 hr·ng/mL, about 6000 hr·ng/mL, about 6500 hr·ng/mL,about 7000 hr·ng/mL, about 7500 hr·ng/mL, about 8000 hr·ng/mL, about8500 hr·ng/mL, about 9000 hr·ng/mL, about 9500 hr·ng/mL, about 10000hr·ng/mL, about 11000 hr·ng/mL, about 12000 hr·ng/mL, about 13000hr·ng/mL, about 14000 hr·ng/mL, about 15000 hr·ng/mL, about 16000hr·ng/mL, about 17000 hr·ng/mL, about 18000 hr·ng/mL, about 19000hr·ng/mL, or about 20000 hr·ng/mL, or any range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the comparable subject at the seventh day ofthe administration is at about 100 hr·ng/mL, about 150 hr·ng/mL, about200 hr·ng/mL, about 250 hr·ng/mL, about 300 hr·ng/mL, about 350hr·ng/mL, about 400 hr·ng/mL, about 450 hr·ng/mL, about 500 hr·ng/mL,about 550 hr·ng/mL, about 600 hr·ng/mL, about 650 hr·ng/mL, about 700hr·ng/mL, about 750 hr·ng/mL, about 800 hr·ng/mL, about 850 hr·ng/mL,about 900 hr·ng/mL, about 950 hr·ng/mL, about 1000 hr·ng/mL, about 1050hr·ng/mL, about 1100 hr·ng/mL, about 1150 hr·ng/mL, about 1200 hr·ng/mL,about 1250 hr·ng/mL, about 1300 hr·ng/mL, about 1350 hr·ng/mL, about1400 hr·ng/mL, about 1450 hr·ng/mL, about 1500 hr·ng/mL, about 1550hr·ng/mL, about 1600 hr·ng/mL, about 1650 hr·ng/mL, about 1700 hr·ng/mL,about 1750 hr·ng/mL, about 1800 hr·ng/mL, about 1850 hr·ng/mL, about1900 hr·ng/mL, about 1950 hr·ng/mL, about 2000 hr·ng/mL, about 2050hr·ng/mL, about 2100 hr·ng/mL, about 2150 hr·ng/mL, about 2200 hr·ng/mL,about 2250 hr·ng/mL, about 2300 hr·ng/mL, about 2350 hr·ng/mL, about2400 hr·ng/mL, about 2450 hr·ng/mL, about 2500 hr·ng/mL, about 2550hr·ng/mL, about 2600 hr·ng/mL, about 2650 hr·ng/mL, about 2700 hr·ng/mL,about 2750 hr·ng/mL, about 2800 hr·ng/mL, about 2850 hr·ng/mL, about2900 hr·ng/mL, about 2950 hr·ng/mL, about 3000 hr·ng/mL, about 3050hr·ng/mL, about 3100 hr·ng/mL, about 3150 hr·ng/mL, about 3200 hr·ng/mL,about 3250 hr·ng/mL, about 3300 hr·ng/mL, about 3350 hr·ng/mL, about3400 hr·ng/mL, about 3450 hr·ng/mL, about 3500 hr·ng/mL, about 3550hr·ng/mL, about 3600 hr·ng/mL, about 3650 hr·ng/mL, about 3700 hr·ng/mL,about 3750 hr·ng/mL, about 3800 hr·ng/mL, about 3850 hr·ng/mL, about3900 hr·ng/mL, about 3950 hr·ng/mL, about 4000 hr·ng/mL, about 4050hr·ng/mL, about 4100 hr·ng/mL, about 4150 hr·ng/mL, about 4200 hr·ng/mL,about 4250 hr·ng/mL, about 4300 hr·ng/mL, about 4350 hr·ng/mL, about4400 hr·ng/mL, about 4450 hr·ng/mL, about 4500 hr·ng/mL, about 4550hr·ng/mL, about 4600 hr·ng/mL, about 4650 hr·ng/mL, about 4700 hr·ng/mL,about 4750 hr·ng/mL, about 4800 hr·ng/mL, about 4850 hr·ng/mL, about4900 hr·ng/mL, about 4950 hr·ng/mL, about 5000 hr·ng/mL, about 5100hr·ng/mL, about 5200 hr·ng/mL, about 5300 hr·ng/mL, about 5400 hr·ng/mL,about 5500 hr·ng/mL, about 5600 hr·ng/mL, about 5700 hr·ng/mL, about5800 hr·ng/mL, about 5900 hr·ng/mL, about 6000 hr·ng/mL, about 6500hr·ng/mL, about 7000 hr·ng/mL, about 7500 hr·ng/mL, about 8000 hr·ng/mL,about 8500 hr·ng/mL, about 9000 hr·ng/mL, about 9500 hr·ng/mL, about10000 hr·ng/mL, about 11000 hr·ng/mL, about 12000 hr·ng/mL, about 13000hr·ng/mL, about 14000 hr·ng/mL, about 15000 hr·ng/mL, about 16000hr·ng/mL, about 17000 hr·ng/mL, about 18000 hr·ng/mL, about 19000hr·ng/mL, or about 20000 hr·ng/mL, or any range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the first day ofthe administration is at about 100 hr·ng/mL, about 150 hr·ng/mL, about200 hr·ng/mL, about 250 hr·ng/mL, about 300 hr·ng/mL, about 350hr·ng/mL, about 400 hr·ng/mL, about 450 hr·ng/mL, about 500 hr·ng/mL,about 550 hr·ng/mL, about 600 hr·ng/mL, about 650 hr·ng/mL, about 700hr·ng/mL, about 750 hr·ng/mL, about 800 hr·ng/mL, about 850 hr·ng/mL,about 900 hr·ng/mL, about 950 hr·ng/mL, about 1000 hr·ng/mL, about 1050hr·ng/mL, about 1100 hr·ng/mL, about 1150 hr·ng/mL, about 1200 hr·ng/mL,about 1250 hr·ng/mL, about 1300 hr·ng/mL, about 1350 hr·ng/mL, about1400 hr·ng/mL, about 1450 hr·ng/mL, about 1500 hr·ng/mL, about 1550hr·ng/mL, about 1600 hr·ng/mL, about 1650 hr·ng/mL, about 1700 hr·ng/mL,about 1750 hr·ng/mL, about 1800 hr·ng/mL, about 1850 hr·ng/mL, about1900 hr·ng/mL, about 1950 hr·ng/mL, about 2000 hr·ng/mL, about 2050hr·ng/mL, about 2100 hr·ng/mL, about 2150 hr·ng/mL, about 2200 hr·ng/mL,about 2250 hr·ng/mL, about 2300 hr·ng/mL, about 2350 hr·ng/mL, about2400 hr·ng/mL, about 2450 hr·ng/mL, about 2500 hr·ng/mL, about 2550hr·ng/mL, about 2600 hr·ng/mL, about 2650 hr·ng/mL, about 2700 hr·ng/mL,about 2750 hr·ng/mL, about 2800 hr·ng/mL, about 2850 hr·ng/mL, about2900 hr·ng/mL, about 2950 hr·ng/mL, about 3000 hr·ng/mL, about 3050hr·ng/mL, about 3100 hr·ng/mL, about 3150 hr·ng/mL, about 3200 hr·ng/mL,about 3250 hr·ng/mL, about 3300 hr·ng/mL, about 3350 hr·ng/mL, about3400 hr·ng/mL, about 3450 hr·ng/mL, about 3500 hr·ng/mL, about 3550hr·ng/mL, about 3600 hr·ng/mL, about 3650 hr·ng/mL, about 3700 hr·ng/mL,about 3750 hr·ng/mL, about 3800 hr·ng/mL, about 3850 hr·ng/mL, about3900 hr·ng/mL, about 3950 hr·ng/mL, about 4000 hr·ng/mL, about 4050hr·ng/mL, about 4100 hr·ng/mL, about 4150 hr·ng/mL, about 4200 hr·ng/mL,about 4250 hr·ng/mL, about 4300 hr·ng/mL, about 4350 hr·ng/mL, about4400 hr·ng/mL, about 4450 hr·ng/mL, about 4500 hr·ng/mL, about 4550hr·ng/mL, about 4600 hr·ng/mL, about 4650 hr·ng/mL, about 4700 hr·ng/mL,about 4750 hr·ng/mL, about 4800 hr·ng/mL, about 4850 hr·ng/mL, about4900 hr·ng/mL, about 4950 hr·ng/mL, about 5000 hr·ng/mL, about 5100hr·ng/mL, about 5200 hr·ng/mL, about 5300 hr·ng/mL, about 5400 hr·ng/mL,about 5500 hr·ng/mL, about 5600 hr·ng/mL, about 5700 hr·ng/mL, about5800 hr·ng/mL, about 5900 hr·ng/mL, about 6000 hr·ng/mL, about 6500hr·ng/mL, about 7000 hr·ng/mL, about 7500 hr·ng/mL, about 8000 hr·ng/mL,about 8500 hr·ng/mL, about 9000 hr·ng/mL, about 9500 hr·ng/mL, about10000 hr·ng/mL, about 11000 hr·ng/mL, about 12000 hr·ng/mL, about 13000hr·ng/mL, about 14000 hr·ng/mL, about 15000 hr·ng/mL, about 16000hr·ng/mL, about 17000 hr·ng/mL, about 18000 hr·ng/mL, about 19000hr·ng/mL, or about 20000 hr·ng/mL, or any range therebetween.

In some embodiments, the resulted AUC of the plasma concentration forthe β-lactam compound in the subject in need thereof at the seventh dayof the administration is at about 100 hr·ng/mL, about 150 hr·ng/mL,about 200 hr·ng/mL, about 250 hr·ng/mL, about 300 hr·ng/mL, about 350hr·ng/mL, about 400 hr·ng/mL, about 450 hr·ng/mL, about 500 hr·ng/mL,about 550 hr·ng/mL, about 600 hr·ng/mL, about 650 hr·ng/mL, about 700hr·ng/mL, about 750 hr·ng/mL, about 800 hr·ng/mL, about 850 hr·ng/mL,about 900 hr·ng/mL, about 950 hr·ng/mL, about 1000 hr·ng/mL, about 1050hr·ng/mL, about 1100 hr·ng/mL, about 1150 hr·ng/mL, about 1200 hr·ng/mL,about 1250 hr·ng/mL, about 1300 hr·ng/mL, about 1350 hr·ng/mL, about1400 hr·ng/mL, about 1450 hr·ng/mL, about 1500 hr·ng/mL, about 1550hr·ng/mL, about 1600 hr·ng/mL, about 1650 hr·ng/mL, about 1700 hr·ng/mL,about 1750 hr·ng/mL, about 1800 hr·ng/mL, about 1850 hr·ng/mL, about1900 hr·ng/mL, about 1950 hr·ng/mL, about 2000 hr·ng/mL, about 2050hr·ng/mL, about 2100 hr·ng/mL, about 2150 hr·ng/mL, about 2200 hr·ng/mL,about 2250 hr·ng/mL, about 2300 hr·ng/mL, about 2350 hr·ng/mL, about2400 hr·ng/mL, about 2450 hr·ng/mL, about 2500 hr·ng/mL, about 2550hr·ng/mL, about 2600 hr·ng/mL, about 2650 hr·ng/mL, about 2700 hr·ng/mL,about 2750 hr·ng/mL, about 2800 hr·ng/mL, about 2850 hr·ng/mL, about2900 hr·ng/mL, about 2950 hr·ng/mL, about 3000 hr·ng/mL, about 3050hr·ng/mL, about 3100 hr·ng/mL, about 3150 hr·ng/mL, about 3200 hr·ng/mL,about 3250 hr·ng/mL, about 3300 hr·ng/mL, about 3350 hr·ng/mL, about3400 hr·ng/mL, about 3450 hr·ng/mL, about 3500 hr·ng/mL, about 3550hr·ng/mL, about 3600 hr·ng/mL, about 3650 hr·ng/mL, about 3700 hr·ng/mL,about 3750 hr·ng/mL, about 3800 hr·ng/mL, about 3850 hr·ng/mL, about3900 hr·ng/mL, about 3950 hr·ng/mL, about 4000 hr·ng/mL, about 4050hr·ng/mL, about 4100 hr·ng/mL, about 4150 hr·ng/mL, about 4200 hr·ng/mL,about 4250 hr·ng/mL, about 4300 hr·ng/mL, about 4350 hr·ng/mL, about4400 hr·ng/mL, about 4450 hr·ng/mL, about 4500 hr·ng/mL, about 4550hr·ng/mL, about 4600 hr·ng/mL, about 4650 hr·ng/mL, about 4700 hr·ng/mL,about 4750 hr·ng/mL, about 4800 hr·ng/mL, about 4850 hr·ng/mL, about4900 hr·ng/mL, about 4950 hr·ng/mL, about 5000 hr·ng/mL, about 5100hr·ng/mL, about 5200 hr·ng/mL, about 5300 hr·ng/mL, about 5400 hr·ng/mL,about 5500 hr·ng/mL, about 5600 hr·ng/mL, about 5700 hr·ng/mL, about5800 hr·ng/mL, about 5900 hr·ng/mL, about 6000 hr·ng/mL, about 6500hr·ng/mL, about 7000 hr·ng/mL, about 7500 hr·ng/mL, about 8000 hr·ng/mL,about 8500 hr·ng/mL, about 9000 hr·ng/mL, about 9500 hr·ng/mL, about10000 hr·ng/mL, about 11000 hr·ng/mL, about 12000 hr·ng/mL, about 13000hr·ng/mL, about 14000 hr·ng/mL, about 15000 hr·ng/mL, about 16000hr·ng/mL, about 17000 hr·ng/mL, about 18000 hr·ng/mL, about 19000hr·ng/mL, or about 20000 hr·ng/mL, or any range therebetween.

Other Effects of the Methods

The method of the present disclosure may result in one or moreadditional effects to the subject in need thereof.

In some embodiments, the administration results a half life of thebeta-lactam compound that is longer in the subject in need thereof ascompared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time.

In some embodiments, the administration results a half life of thebeta-lactam compound that is about 10%, about 20%, about 30%, about 40%,about 50%, about 60%, about 70%, about 80%, about 90%, about 100%, about200%, about 300%, about 400%, or about 500% longer in the subject inneed thereof as compared to a comparable subject being administered tothe pharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time.

In some embodiments, the administration results a time over minimuminhibitory concentration (MIC) for the beta-lactam compound that islonger in the subject in need thereof as compared to a comparablesubject being administered to the pharmaceutically effective amount ofthe β-lactam compound without probenecid over the period of time.

In some embodiments, the administration results a time over MIC for thebeta-lactam compound that is about 10%, about 20%, about 30%, about 40%,about 50%, about 60%, about 70%, about 80%, about 90%, about 100%, about200%, about 300%, about 400%, or about 500% longer in the subject inneed thereof as compared to a comparable subject being administered tothe pharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time.

In some embodiments, the administration of the probenecid or apharmaceutically acceptable salt thereof does not substantially increasethe elimination rate of the β-lactam compound or a pharmaceuticallyacceptable salt thereof in the subject in need thereof.

In some embodiments, the elimination rate of the β-lactam compound or apharmaceutically acceptable salt thereof in the subject in need thereofis about 150% or less, about 120% or less, about 110% or less, about105% or less, about 103% or less, or about 101% or less, as compared tothe comparable subject.

In some embodiments, the elimination rate of the β-lactam compound or apharmaceutically acceptable salt thereof in the subject in need thereofis about the same as compared to the comparable subject.

In some embodiments, the administration of the probenecid or apharmaceutically acceptable salt thereof enhances the absorption rate ofthe β-lactam compound or a pharmaceutically acceptable salt thereof inthe subject in need thereof.

In some embodiments, the absorption rate of the β-lactam compound or apharmaceutically acceptable salt thereof in the subject in need thereofis higher as compared to the comparable subject an amount ranging fromabout 2% to about 100%, from about 4% to about 80%, from about 6% toabout 60%, from about 8% to about 40%, from about 10% to about 30%, fromabout 12% to about 25%, or from about 15% to about 20%.

Treated Subjects and Diseases

In some embodiments, the subject in need thereof is an animal. In someembodiments, the subject in need thereof is a human.

In some embodiments, the subject in need thereof is a human of 18 yearsor older.

In some embodiments, the subject in need thereof is a human younger than18 years.

In some embodiments, the disease is associated with an increased ordecreased population of one or more microorganisms (e.g., bacteria) inthe subject.

In some embodiments, the disease is associated with an increasedpopulation of one or more microorganisms (e.g., bacteria) in thesubject. In some embodiments, the method of the present disclosureresults in a decrease population of the one or more microorganisms(e.g., bacteria) in the subject.

In some embodiments, the disease is associated with a decreasedpopulation of one or more microorganisms (e.g., bacteria) in thesubject. In some embodiments, the method of the present disclosureresults in an increased population of the one or more microorganisms(e.g., bacteria) in the subject.

In some embodiments, the disease is associated with an increased ordecreased population of one or more bacteria selected from Escherichiacoli, Klebsiella pneumoniae, Proteus mirabilis, Enterobacter cloacae,Klebsiella oxytoca, Citrobacter freundii complex, Clostridiumclostridioforme, Eubacterium lentum, Peptostreptococcus species,Bacteroides fragilis, Bacteroides distasonis, Bacteroides ovatus,Bacteroides thetaiotaomicron, Bacteroides uniformis, Bacteroidescoprocola, Prevotella copri, Porphyromonas asaccharolytica, andPrevotella bivia or any organisms in the following genera:Succinivibrio, Alistipes, Prevotella, Paraprevotella, Parabacteroides,and Odoribacter.

In some embodiments, the disease is associated with an increased ordecreased pupolation of one or more bacteria selected fromStaphylococcus epidermidis, Streptococcus pneumonia, Staphylococcusaureus, Streptococcus agalactiae, and Streptococcus pyogenes.

In some embodiments, the disease is associated with an increased ordecreased population of one or more bacteria selected from Citrobacterfreundii, Citrobacter koseri, Enterobacter aerogenes, Enterobactercloacae, Haemophilus influenza, Haemophilus parainfluenzae, Klebsiellaoxytoca, Moraxella catarrhalis, Morganella morganii, Proteus vulgaris,Providencia rettgeri, Providencia stuartii, and Serratia marcescens.

In some embodiments, the disease is associated with an increased ordecreased pupolation of one or more bacteria selected from Bacteroidesvulgatus, Clostridium perfringens, and Fusobacterium spp.

In some embodiments, the disease is associated with an infection. Insome embodiments, the infection is a gram-negative infection. In someembodiments, the infection is a gram-positive infection.

In some embodiments, the infection is resistant to one or moreantibiotics when being administered without probenecid or thepharmaceutically acceptable salt thereof.

In some embodiments, the infection is resistant to one or more β-lactamcompounds when being administered without probenecid or thepharmaceutically acceptable salt thereof.

In some embodiments, the disease is an uncomplicated urinary tractinfection, a complicated urinary tract infection, a complicatedintra-abdominal infection, an uncomplicated intra-abdominal infection,pneumonia, otitis media, sinusitis, gonococcal urethritis, pelvicinflammatory disease, prostatitis, bone infection, joint infection,diabetic foot infection and infectious diarrhea.

In some embodiments, the disease is associated with (e.g., resultedfrom) the alteration of the microbiome in the subject.

In some embodiments, the disease is associated with (e.g., resultedfrom) the alteration of the microbiome in the human subject.

In some embodiments, the disease is a neurodegenerative disease.

In some embodiments, the disease is amyotrophic lateral sclerosis,Parkinson's disease, Alzheimer's disease, schizophrenia or Huntington'sdisease.

In some embodiments, the disease is Alzheimer's disease. It is notedthat probenecid has been found to increase the concentrations ofβ-lactam compounds in the cerebrospinal fluid (Ralph G. Dacey and MerleA. Sande, Antimicrobial Agents and Chemotherapy 6:437-441 (1974)). Morerecently, a bacterial pathogen, Porphyromonas gingivalis, has been foundin brain in association with pathologic lesions, which are associatedwith Alzheimer's disease (Dominy et al., Sci. Adv. 5:eaau3333 (2019),and sulopenem is active against this bacterium (Lois M. Ednie and PeterC. Appelbaum, Antimicrobial Agents and Chemotherapy 53: 2163-2170(2009)). Without wishing to be bound by theory, it is understood thatthe beta-lactam compounds (e.g., Compound III-2b), when being dosed withprobenecid, may lead to more effective treatment of a brain infectionwith this organism relative to treatment with sulopenem alone.

In some embodiments, the disease is cancer.

In some embodiments, the cancer is a solid cancer, e.g., ovarian cancer,breast cancer, head and neck cancer, renal cancer, bladder cancer,hepatocellular cancer, colorectal cancer, or lymphoma, or anycombination thereof.

In some embodiments, the cancer is sarcoma or carcinoma, e.g.,fibrosarcoma, myxosarcoma, liposarcoma, chondrosarcoma, osteogenicsarcoma, chordoma, angiosarcoma, endotheliosarcoma, lymphangiosarcoma,lymphangioendotheliosarcoma, synovioma, mesothelioma, Ewing's tumor,leiomyosarcoma, rhabdomyosarcoma, colon carcinoma, pancreatic cancer,prostate cancer, squamous cell carcinoma, basal cell carcinoma,adenocarcinoma, sweat gland carcinoma, sebaceous gland carcinoma,papillary carcinoma, papillary adenocarcinomas, cystadenocarcinoma,medullary carcinoma, bronchogenic carcinoma, hepatoma, bile ductcarcinoma, choriocarcinoma, seminoma, embryonal carcinoma, Wilms' tumor,cervical cancer, testicular tumor, lung carcinoma, small cell lungcarcinoma, epithelial carcinoma, glioma, astrocytoma, medulloblastoma,craniopharyngioma, ependymoma, pinealoma, hemangioblastoma, acousticneuroma, oligodendroglioma, meningioma, melanoma, neuroblastoma,retinoblastoma.

In some embodiments, the cancer is leukemia, e.g., acute lymphocyticleukemia and acute myelocytic leukemia (myeloblastic, promyelocytic,myelomonocytic, monocytic and erythroleukemia); or chronic leukemia(chronic myelocytic (granulocytic) leukemia and chronic lymphocyticleukemia).

In some embodiments, the cancer is polycythemia vera, lymphoma(Hodgkin's disease and non-Hodgkin's disease), multiple myeloma,Waldenstrom's macroglobulinemia, or heavy chain disease.

In some embodiments, the disease is an inflammatory bowel disease.

In some embodiments, the inflammatory bowel disease is Crohn's disease,ulcerative colitis, indeterminate colitis, irritable bowel syndrome,microscopic colitis, deversion colitis, or Behcet's disease.

β-Lactam Compounds

In some embodiments, the β-lactam compound is a monobactam or a prodrugthereof.

In some embodiments, the β-lactam compound is aztreonam, tigemonam,carumonam, nocardicin A, a prodrug thereof, an analog thereof, or aderivative thereof.

In some embodiments, the β-lactam compound is a penem, a carbapenem, aclavam, or a prodrug thereof.

In some embodiments, the β-lactam compound is benzylpenicillin,benzathine benzylpenicillin, procaine benzylpenicillin,phenoxymethylpenicillin, propicillin, pheneticillin, azidocillin,clometocillin, penamecillin, cloxacillin (e.g., dicloxacillin orflucloxacillin), oxacillin, nafcillin, methicillin, amoxicillin,ampicillin (e.g., pivampicillin, hetacillin, bacampicillin,metampicillin, talampicillin), epicillin, ticarcillin, carbenicillin,carindacillin, temocillin, piperacillin, azlocillin, mezlocillin,mecillinam (e.g., pivmecillinam), sulbenicillin, a pharmaceuticallyacceptable salt thereof, a prodrug thereof, an analog thereof, or aderivative thereof.

In some embodiments, the β-lactam compound is a penem, a carbapenem, ora prodrug thereof.

In some embodiments, the β-lactam compound a thiopenem, an oxypenem, anaminopenem, an alkylpenems, an arylpenem, or a prodrug thereof.

In some embodiments, the β-lactam compound is ertapenem, anantipseudomonal carbapenem (e.g., doripenem, imipenem, meropenem),biapenem, panipenem, sulopenem, tebipenem, faropenem, a pharmaceuticallyacceptable salt thereof, a prodrug thereof, an analog thereof, or aderivative thereof.

In some embodiments, the β-lactam compound is a cephem, a carbacephem,an oxacephem, or a prodrug thereof.

In some embodiments, the β-lactam compound is cefazolin, cefalexin,cefadroxil, cefapirin, cefazedone, cefazaflur, cefradine, cefroxadine,ceftezole, cefaloglycin, cefacetrile, cefalonium, cefaloridine,cefalotin, cefatrizine, cefaclor, cefotetan, cephamycin (e.g.,cefoxitin, cefprozil, cefuroxime, cefuroxime axetil, cefamandole,cefminox, cefonicid, ceforanide, cefotiam, cefbuperazone, cefuzonam,cefmetazole), carbacephem (e.g., loracarbef), cefixime, ceftriaxone,antipseudomonal (e.g, ceftazidime, cefoperazone), cefdinir, cefcapene,cefdaloxime, ceftizoxime, cefmenoxime, cefotaxime, cefpiramide,cefpodoxime, ceftibuten, cefditoren, cefetamet, cefodizime, cefpimizole,cefsulodin, cefteram, ceftiolene, oxacephem (e.g., flomoxef, latamoxef),cefepime, cefozopran, cefpirome, cefquinome, ceftaroline fosamil,ceftolozane, ceftobiprole, ceftiofur, cefquinome, cefovecin, apharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the β-lactam compound is a thiopenem or a prodrugthereof.

In some embodiments, the β-lactam compound is of Formula (I):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R¹ is H or optionallysubstituted alkyl.

In some embodiments, the β-lactam compound is of Formula (Ia):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the β-lactam compound is of Formula (Ib):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, R¹ is H.

In some embodiments, the β-lactam compound is of Formula (II):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the β-lactam compound is of Formula (IIa):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the β-lactam compound is of Formula (IIb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, R¹ is optionally substituted alkyl.

In some embodiments, the β-lactam compound is of any one of Formulae(III), (IIIa), and (IIIb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R² is H or optionallysubstituted alkyl.

In some embodiments, the β-lactam compound is selected from the groupconsisting of:

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof.

In some embodiments, the j-lactam compound is selected from the groupconsisting of:

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof.

In some embodiments, the β-lactam compound is selected from

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof.

In some embodiments, the β-lactam compound is

In some embodiments, the β-lactam compound is of any one of Formulae(IV), (IVa), and (IVb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R³ is H or optionallysubstituted alkyl.

In some embodiments, R³ is C₂-C₈ alkyl.

In some embodiments, R³ is CH₂CH₃, CH₂CH₂CH₃, or CH₂CH(CH₃)₂.

Administrations of β-Lactam Compounds and Probenecid

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered simultaneously.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered by enteral administration.

In some embodiments, the enteral administration is oral administration.

In some embodiments, an oral co-formulation comprising the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof is administered.

In some embodiments, a tablet comprising the β-lactam compound or thepharmaceutically acceptable salt thereof and probenecid or thepharmaceutically acceptable salt thereof is administered.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered in separate oralformulations.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered in separate tablets.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered by parenteraladministration.

In some embodiments, the parenteral administration is intravenousadministration.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered in a co-formulation.

In some embodiments, the co-formulation is administered to the subjectone or more times daily.

In some embodiments, the co-formulation is an oral co-formulation (e.g.,a tablet).

In some embodiments, the oral co-formulation comprises:

from 20 mg to about 5 g, from about 50 mg to about 2 g, from about 80 mgto about 1 g, from about 100 mg to about 900 mg, from about 200 mg toabout 800 mg, from about 300 mg to about 700 mg, from about 400 mg toabout 600 mg, from about 450 mg to about 550 mg, or from about 480 mg toabout 520 mg of the β-lactam compound or the pharmaceutically acceptablesalt thereof; and from 20 mg to about 5 g, from about 50 mg to about 2g, from about 80 mg to about 1 g, from about 100 mg to about 900 mg,from about 200 mg to about 800 mg, from about 300 mg to about 700 mg,from about 400 mg to about 600 mg, from about 450 mg to about 550 mg, orfrom about 480 mg to about 520 mg of probenecid or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the oral co-formulation comprises about 500 mg ofthe β-lactam compound or the pharmaceutically acceptable salt thereofand about 500 mg of probenecid or the pharmaceutically acceptable saltthereof.

In some embodiments, the oral co-formulation is administered to thesubject once daily, two times daily, three times daily, or four timesdaily for about 1 day, about 2 days, about 3 days, about 4 days, about 5days, about 6 days, about 7 days, about 14 days, about 21 days, or about28 days.

In some embodiments, the oral co-formulation is administered to thesubject two times daily for about 5 days.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered in separate formulations.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered simultaneously, sequentially,or in alternation.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered simultaneously.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered sequentially.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered in temporal proximity.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered prior to the administration ofprobenecid or the pharmaceutically acceptable salt thereof.

In some embodiments, probenecid or the pharmaceutically acceptable saltthereof is administered prior to the administration of the β-lactamcompound or the pharmaceutically acceptable salt thereof.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered or in alternation.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered one or more times daily at adaily dosage ranging from about 20 mg to about 5 g, from about 50 mg toabout 2 g, from about 80 mg to about 1 g, from about 100 mg to about 900mg, from about 200 mg to about 800 mg, from about 300 mg to about 700mg, from about 400 mg to about 600 mg, from about 450 mg to about 550mg, or from about 480 mg to about 520 mg.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered one or more times daily at adaily dosage at about 500 mg.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered one or more times daily at adaily dosage ranging from about 50 mg to about 10 g, from about 100 mgto about 5 g, from about 200 mg to about 3 g, from about 400 mg to about2 g, from about 600 mg to about 1.5 g, from about 800 mg to about 1.2 g,or from about 900 mg to about 1.1 g.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered one or more times daily at adaily dosage at about 1 g.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered one or more times daily at adaily dosage ranging from about 100 mg to about 10 g, from about 200 mgto about 5 g, from about 500 mg to about 3 g, from about 800 mg to about2.5 g, from about 1 g to about 2 g, from about 1.2 g to about 1.8 g, orfrom about 1.4 g to about 1.6 g.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered on or more times daily at adaily dosage at about 1.5 g.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered once daily.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered twice daily.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered three or more times daily.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered continuously.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered for more than about 1 day.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered for about 2 days, about 3 days,about 4 days, about 5 days, about 6 days, about 7 days, about 14 days,or about 30 days.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered with one or more drug holidays.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered without any drug holiday.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered by an enteral administration.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered by an oral administration or arectum administration.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered by an oral administration.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered by a parenteral administration.

In some embodiments, the β-lactam compound or the pharmaceuticallyacceptable salt thereof is administered by an intravenousadministration. In some embodiments, an injectable formulation of theβ-lactam compound or the pharmaceutically acceptable salt thereof isadministered to the subject.

In some embodiments, the injectable formulation is an intravenousinfusion.

In some embodiments, the injectable formulation comprises about 50 mg toabout 10 g, from about 100 mg to about 5 g, from about 200 mg to about 3g, from about 400 mg to about 2 g, from about 600 mg to about 1.5 g,from about 800 mg to about 1.2 g, or from about 900 mg to about 1.1 g ofthe β-lactam compound or the pharmaceutically acceptable salt thereof.

In some embodiments, the injectable formulation comprises about 1 g ofthe β-lactam compound or the pharmaceutically acceptable salt thereof.

In some embodiments, the injectable formulation is administered to thesubject by intravenous infusion over about 30 minutes, about 1 hour,about 2 hours, about 3 hours, about 4 hours, about 6 hours, or about 12hours.

In some embodiments, the injectable formulation is administered to thesubject by intravenous infusion over about 3 hours.

In some embodiments, the injectable formulation is administered to thesubject once every 6 hours, once every 12 hours, once every 24 hours,once every hours, or once ever 48 hours, for from about 1 day to about30 days, from about 2 days to about 28 days, from about 3 days to about24 days, from about 4 days to about 21 days, from about 5 days to about18 days, from about 6 days to about 15 days, or from about 7 days toabout 14 days.

In some embodiments, the injectable formulation is administered to thesubject once every 24 hours for about 7 days, about 8 days, about 9days, about 10 days, about 11 days, about 12 days, about 13 days, orabout 14 days.

In some embodiments, the subject has renal impairment, and wherein:

the injectable formulation comprises from about 10 mg to about 2 g, fromabout 25 mg to about 1 g, from about 40 mg to about 500 mg, from about50 mg to about 450 mg, from about 100 mg to about 400 mg, from about 150mg to about 350 mg, from about 200 mg to about 300 mg, from about 225 mgto about 275 mg, or from about 240 mg to about 260 mg of the β-lactamcompound or the pharmaceutically acceptable salt thereof;

the injectable formulation is administered to the subject by intravenousinfusion over about 30 minutes, about 1 hour, about 2 hours, about 3hours, about 4 hours, about 6 hours, or about 12 hours; and theinjectable formulation is administered to the subject once every 6hours, once every 12 hours, once every 24 hours, once every hours, oronce ever 48 hours.

In some embodiments, the subject has renal impairment, and wherein:

the injectable formulation comprises about 250 mg of the β-lactamcompound or the pharmaceutically acceptable salt thereof;

the injectable formulation is administered to the subject once every 24hours by intravenous infusion over about 3 hours.

In some embodiments, the subject in need thereof is not fasted withinabout 1 hour, about 2 hours, about 3 hours, about 6 hours, about 12hours, about 24 hours, about 2 days, about 5 days, or about 10 daysprior to administration of the β-lactam compound or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the subject in need thereof is fasted for about 1hour, about 2 hours, about 3 hours, about 6 hours, about 12 hours, about24 hours, about 2 days, about 5 days, or about 10 days prior toadministration of the β-lactam compound or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the subject in need thereof is not fasted withinabout 1 hour, about 2 hours, about 3 hours, about 6 hours, about 12hours, about 24 hours, about 2 days, about 5 days, or about 10 daysafter administration of the β-lactam compound or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the subject in need thereof is fasted for about 1hour, about 2 hours, about 3 hours, about 6 hours, about 12 hours, about24 hours, about 2 days, about 5 days, or about 10 days afteradministration of the β-lactam compound or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageranging from about 20 mg to about 5 g, from about 50 mg to about 2 g,from about 80 mg to about 1 g, from about 100 mg to about 900 mg, fromabout 200 mg to about 800 mg, from about 300 mg to about 700 mg, fromabout 400 mg to about 600 mg, from about 450 mg to about 550 mg, or fromabout 480 mg to about 520 mg.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageat about 500 mg.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageranging from about 50 mg to about 10 g, from about 100 mg to about 5 g,from about 200 mg to about 3 g, from about 400 mg to about 2 g, fromabout 600 mg to about 1.5 g, from about 800 mg to about 1.2 g, or fromabout 900 mg to about 1.1 g.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageat about 1 g.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageranging from about 100 mg to about 10 g, from about 200 mg to about 5 g,from about 500 mg to about 3 g, from about 800 mg to about 2.5 g, fromabout 1 g to about 2 g, from about 1.2 g to about 1.8 g, or from about1.4 g to about 1.6 g.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered one or more times daily at a daily dosageat about 1.5 g.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered once daily.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered twice daily.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered three or more times daily.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered continuously.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered for more than about 1 day.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered for about 2 days, about 3 days, about 4days, about 5 days, about 6 days, about 7 days, about 14 days, or about30 days.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered with one or more drug holidays.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered without any drug holiday.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered by an enteral administration.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered by an oral administration or a rectumadministration.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered by an oral administration.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered by a parenteral administration.

In some embodiments, the probenecid or the pharmaceutically acceptablesalt thereof is administered by an intravenous administration.

In some embodiments, the subject in need thereof is not fasted withinabout 1 hour, about 2 hours, about 3 hours, about 6 hours, about 12hours, about 24 hours, about 2 days, about 5 days, or about 10 daysprior to administration of the probenecid or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the subject in need thereof is fasted for about 1hour, about 2 hours, about 3 hours, about 6 hours, about 12 hours, about24 hours, about 2 days, about 5 days, or about 10 days prior toadministration of the probenecid or the pharmaceutically acceptable saltthereof.

In some embodiments, the subject in need thereof is not fasted withinabout 1 hour, about 2 hours, about 3 hours, about 6 hours, about 12hours, about 24 hours, about 2 days, about 5 days, or about 10 daysafter administration of the probenecid or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the subject in need thereof is fasted for about 1hour, about 2 hours, about 3 hours, about 6 hours, about 12 hours, about24 hours, about 2 days, about 5 days, or about 10 days afteradministration of the probenecid or the pharmaceutically acceptable saltthereof.

Alternatives Uses of β-Lactam Compounds and Probenecids

In some aspects, the present disclosure provides a β-lactam compound ora pharmaceutically acceptable salt thereof for use in combination withprobenecid or a pharmaceutically acceptable salt thereof in treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides probenecid or apharmaceutically acceptable salt thereof for use in combination with aβ-lactam compound or a pharmaceutically acceptable salt thereof intreating or preventing a disease in a subject in need thereof, whereinthe β-lactam compound or the pharmaceutically acceptable salt thereofand probenecid or the pharmaceutically acceptable salt thereof areadministered to the subject by the same administration route.

In some aspects, the present disclosure provides a combination of aβ-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof for use intreating or preventing a disease in a subject in need thereof, whereinthe β-lactam compound or the pharmaceutically acceptable salt thereofand probenecid or the pharmaceutically acceptable salt thereof areadministered to the subject by the same administration route.

In some aspects, the present disclosure provides use of a β-lactamcompound in combination with probenecid or a pharmaceutically acceptablesalt thereof in the manufacture of a medicament for treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides use of probenecid incombination with a β-lactam compound or a pharmaceutically acceptablesalt thereof in the manufacture of a medicament for treating orpreventing a disease in a subject in need thereof, wherein the β-lactamcompound or the pharmaceutically acceptable salt thereof and probenecidor the pharmaceutically acceptable salt thereof are administered to thesubject by the same administration route.

In some aspects, the present disclosure provides use of a combination ofa β-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease in asubject in need thereof, wherein the β-lactam compound or thepharmaceutically acceptable salt thereof and probenecid or thepharmaceutically acceptable salt thereof are administered to the subjectby the same administration route.

In some aspects, the present disclosure provides a β-lactam compound ora pharmaceutically acceptable salt thereof for use in combination withprobenecid or a pharmaceutically acceptable salt thereof in treating orpreventing a disease, wherein: the β-lactam compound or thepharmaceutically acceptable salt thereof and the probenecid or apharmaceutically acceptable salt thereof are administered to a subjectin need over a period of time, wherein the administration results in aplasma concentration for the β-lactam compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides probenecid or apharmaceutically acceptable salt thereof for use in combination with aβ-lactam compound or a pharmaceutically acceptable salt thereof intreating or preventing a disease, wherein:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides a combination of aβ-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof for use intreating or preventing a disease, wherein:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of a β-lactamcompound or a pharmaceutically acceptable salt thereof in combinationwith probenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of probenecid or apharmaceutically acceptable salt thereof in combination with a β-lactamcompound or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

In some aspects, the present disclosure provides use of a combination ofa β-lactam compound or a pharmaceutically acceptable salt thereof andprobenecid or a pharmaceutically acceptable salt thereof in themanufacture of a medicament for treating or preventing a disease,wherein administration of the medicament to a subject in need over aperiod of time results in a plasma concentration for the β-lactamcompound having:

the β-lactam compound or the pharmaceutically acceptable salt thereofand the probenecid or a pharmaceutically acceptable salt thereof areadministered to a subject in need over a period of time, wherein theadministration results in a plasma concentration for the β-lactamcompound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered to thepharmaceutically effective amount of the β-lactam compound withoutprobenecid over the period of time,

a maximum plasma concentration (C_(max)) that is higher in the subjectin need thereof as compared to the comparable subject being administeredto the pharmaceutically effective amount of the β-lactam compoundwithout probenecid over the period of time, or

a combination thereof.

Exemplary Methods

In some aspects, the present disclosure provides a method of treating orpreventing a disease, comprising administering to a subject in needthereof an oral co-formulation of about 500 mg of Compound III-2b andabout 500 mg of probenecid, wherein the administration results in aplasma concentration for Compound III-2b having: an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with Compound III-2b andprobenecid by different administration routes by about 20% or greaterwithin about 1 day from the administration; and

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with Compound III-2b and probenecid by differentadministration routes.

In some aspects, the present disclosure provides a method of treating orpreventing a disease, comprising administering to a subject in needthereof an oral co-formulation of about 500 mg of Compound III-2b andabout 500 mg of probenecid, wherein the administration results in aplasma concentration for Compound III-2b having an area under the curve(AUC) being from about 4800 ng·h/mL to about 4850 ng·h/mL within about12 hours from the administration and a maximum plasma concentration(C_(max)) of Compound III-2b being from about 1800 ng/mL to about 1850ng/mL.

In some aspects, the present disclosure provides a method of treating orpreventing a disease, comprising administering to a subject in needthereof an oral co-formulation of about 500 mg of Compound III-2b andabout 500 mg of probenecid, wherein the administration results in aplasma concentration for Compound III-2b having an area under the curve(AUC) being from about 7550 ng·h/mL to about 8000 ng·h/mL within about12 hours from the administration and a maximum plasma concentration(C_(max)) of Compound III-2b being from about 2650 ng/mL to about 2700ng/mL.

Pharmaceutical Compositions and Pharmaceutical Kits

In some aspects, the present disclosure provides a pharmaceuticalcomposition comprising a β-lactam compound or a pharmaceuticallyacceptable salt thereof and probenecid or a pharmaceutically acceptablesalt thereof.

In some embodiments, the pharmaceutical composition is in an oral dosageform.

In some embodiments, the pharmaceutical composition comprises:

from 20 mg to about 5 g, from about 50 mg to about 2 g, from about 80 mgto about 1 g, from about 100 mg to about 900 mg, from about 200 mg toabout 800 mg, from about 300 mg to about 700 mg, from about 400 mg toabout 600 mg, from about 450 mg to about 550 mg, or from about 480 mg toabout 520 mg of the β-lactam compound or the pharmaceutically acceptablesalt thereof; and from 20 mg to about 5 g, from about 50 mg to about 2g, from about 80 mg to about 1 g, from about 100 mg to about 900 mg,from about 200 mg to about 800 mg, from about 300 mg to about 700 mg,from about 400 mg to about 600 mg, from about 450 mg to about 550 mg, orfrom about 480 mg to about 520 mg of probenecid or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the pharmaceutical composition comprises about 500mg of the β-lactam compound or the pharmaceutically acceptable saltthereof; and about 500 mg of probenecid or the pharmaceuticallyacceptable salt thereof.

In some embodiments, the pharmaceutical composition comprises about 500mg of Compound III-2b and about 500 mg of probenecid.

In some embodiments, the pharmaceutical composition, when beingadministered to a subject in need thereof, results in one or more of theeffects disclosed herein (e.g., the AUC and/or C_(max) for the β-lactamcompound disclosed herein).

In some aspects, the present disclosure provides a pharmaceutical kitcomprising a β-lactam compound or a pharmaceutically acceptable saltthereof in a first package and probenecid or a pharmaceuticallyacceptable salt thereof in a second package.

In some embodiments, at least one of the β-lactam compound or thepharmaceutically acceptable salt thereof or the probenecid or thepharmaceutically acceptable salt thereof is in an oral dosage form;

preferably, the β-lactam compound or the pharmaceutically acceptablesalt thereof is in an oral dosage form, or the probenecid or thepharmaceutically acceptable salt thereof is in an oral dosage form;

more preferably, both of the β-lactam compound or the pharmaceuticallyacceptable salt thereof and the probenecid or the pharmaceuticallyacceptable salt thereof are in oral dosage forms.

In some embodiments, the pharmaceutical kit, when being used by asubject in need thereof, results in one or more of the effects disclosedherein (e.g., the AUC and/or C_(max) for the β-lactam compound disclosedherein).

In some embodiments, the pharmaceutical kit comprises:

from 20 mg to about 5 g, from about 50 mg to about 2 g, from about 80 mgto about 1 g, from about 100 mg to about 900 mg, from about 200 mg toabout 800 mg, from about 300 mg to about 700 mg, from about 400 mg toabout 600 mg, from about 450 mg to about 550 mg, or from about 480 mg toabout 520 mg of the β-lactam compound or the pharmaceutically acceptablesalt thereof in the first package; and from 20 mg to about 5 g, fromabout 50 mg to about 2 g, from about 80 mg to about 1 g, from about 100mg to about 900 mg, from about 200 mg to about 800 mg, from about 300 mgto about 700 mg, from about 400 mg to about 600 mg, from about 450 mg toabout 550 mg, or from about 480 mg to about 520 mg of probenecid or thepharmaceutically acceptable salt thereof in the second package.

In some embodiments, the pharmaceutical composition comprises about 500mg of the β-lactam compound or the pharmaceutically acceptable saltthereof in the first package; and about 500 mg of probenecid or thepharmaceutically acceptable salt thereof in the second package.

In some embodiments, the pharmaceutical composition comprises about 500mg of Compound III-2b in the first package and about 500 mg ofprobenecid in the second package.

Other Suitable Compounds

In some aspects, the present disclosure provides a compound or apharmaceutical salt thereof, wherein administration of the compound orthe pharmaceutical salt thereof in combination with probenecid or apharmaceutically acceptable salt thereof into a subject in need thereofby the same administration route results in a plasma concentrationversus time curve for the compound having:

an area under the curve (AUC) that is higher in the subject in needthereof as compared to a comparable subject being administered with thecompound and probenecid by different administration routes;

a maximum plasma concentration (C_(max)) in the subject in need thereofthat is substantially the same as compared to a comparable subject beingadministered with the compound and probenecid by differentadministration routes; or

a combination thereof.

In some aspects, the present disclosure provides a compound or apharmaceutical salt thereof, wherein administration of the compound orthe pharmaceutical salt thereof in combination with probenecid or apharmaceutically acceptable salt thereof into a subject in need thereofover a period of time results in a plasma concentration versus timecurve for the compound having: an area under the curve (AUC) that ishigher in the subject in need thereof as compared to a comparablesubject being administered to the pharmaceutically effective amount ofthe compound without probenecid over the period of time,

a maximum plasma concentration (C_(max)) for the compound that is higherin the subject in need thereof as compared to the comparable subjectbeing administered to the pharmaceutically effective amount of thecompound without probenecid over the period of time, or

a combination thereof.

In some embodiments, the compound is selected from the group consistingof:

-   -   Latanoprost acid    -   PGH₂    -   PGE₁    -   PGE₂    -   PGF_(2α)    -   Thromboxane B₂        pharmaceutically acceptable salts thereof, prodrugs thereof,        analogs thereof, and derivatives thereof.

In some embodiments, the compound is selected from the group consistingof:

-   -   Aliskiern    -   Atorvastatin    -   Benzylpenicillin    -   BDE47    -   BDE99    -   BDE153    -   Bosentan    -   Bromosulphophthalein    -   CP-671,305    -   Dehydroepiandrosterone-3-sulphate    -   Eltrombopag    -   Estrone-3-sulphate    -   Ezetimibe glucuronide    -   Fexofenadine    -   Fluvastatin    -   Glibenclamide    -   Latanoprost add    -   M17055    -   Mesalazine    -   Montelukast    -   Pravastatin    -   Pitavastatin    -   Pregnenolone sulphate    -   PGE₂    -   Rosuvastatin    -   Talinolol    -   Taurocholate    -   Tebipenem pivoxil    -   Thyroxine (T4)    -   Unoprostone metabolite        pharmaceutically acceptable salts thereof, prodrugs thereof,        analogs thereof, and derivatives thereof.

In some embodiments, the compound is selected from the group consistingof:

-   -   Acebutolol    -   APD-ajmalinium    -   Ateriolol    -   Arasentan    -   Bamet-R2    -   Bamet-UD2    -   Bilirubin    -   BQ-123    -   Bromosulphophthalein    -   Celiprolol    -   Chlorambucil-taurocholate    -   Cholate    -   Ciprolloxacin    -   CRC220    -   Darunavir    -   Dehydroepiandrosterone-3-sulphate    -   Deltorphin II    -   [D-penicillamine^(2,3)]enkephalin    -   Enoxacin    -   Epicatechin gallate    -   Epigallocatechin gate    -   Erythromycin    -   Estradiol-17β-glucuronide    -   Estrone-3-sulphate    -   Fexofenadine    -   Gatifloxacin    -   Gd-B20790    -   Glycocholate    -   Hydroxyurea    -   Imatinib    -   Labetalol    -   Levofloxacin    -   Lomefloxacin    -   Lopinvair    -   Methotrexate    -   Microcystin    -   N-methylquinidine    -   N-methylquinine    -   Nadolol    -   Norfloxacin    -   Ouabain    -   Pitavastatin    -   PGE₂    -   Reverse triiodothyronine (rT3)    -   Rocuronium    -   Rosuvastatin    -   Saquinavir    -   Sotalol    -   Talinolol    -   Taurocholate    -   Taurochenodeoxycholate    -   Tauroursodeoxycholate    -   Thyroxine (T4)    -   Tebipenem pivoxil    -   TR-14035    -   Triiodothyronine (T3)    -   Unoprostane metabolite        pharmaceutically acceptable salts thereof, prodrugs thereof,        analogs thereof, and derivatives thereof.

In some embodiments, the compound is a monobactam.

In some embodiments, the compound is aztreonam tigemonam, carumonam,nocardicin A, an analog thereof, or a derivative thereof.

In some embodiments, the compound is a penem, a carbapenem, or a clavam.

In some embodiments, the compound is benzylpenicillin, benzathinebenzylpenicillin, procaine benzylpenicillin, phenoxymethylpenicillin,propicillin, pheneticillin, azidocillin, clometocillin, penamecillin,cloxacillin (e.g., dicloxacillin or flucloxacillin), oxacillin,nafcillin, methicillin, amoxicillin, ampicillin (e.g., pivampicillin,hetacillin, bacampicillin, metampicillin, talampicillin), epicillin,ticarcillin, carbenicillin, carindacillin, temocillin, piperacillin,azlocillin, mezlocillin, mecillinam (e.g., pivmecillinam),sulbenicillin, a pharmaceutically acceptable salt thereof, a prodrugthereof, an analog thereof, or a derivative thereof.

In some embodiments, the compound is a penem or a carbapenem.

In some embodiments, the compound is a thiopenem, an oxypenem, anaminopenem, an alkylpenems, or an arylpenem.

In some embodiments, the compound is ertapenem, antipseudomonal (e.g.,doripenem, imipenem, meropenem), biapenem, panipenem, sulopenem, apharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the compound is a cephem, a carbacephem, or anoxacephem.

In some embodiments, the compound is cefazolin, cefalexin, cefadroxil,cefapirin, cefazedone, cefazaflur, cefradine, cefroxadine, ceftezole,cefaloglycin, cefacetrile, cefalonium, cefaloridine, cefalotin,cefatrizine, cefaclor, cefotetan, cephamycin (e.g., cefoxitin,cefprozil, cefuroxime, cefuroxime axetil, cefamandole, cefminox,cefonicid, ceforanide, cefotiam, cefbuperazone, cefuzonam, cefmetazole),carbacephem (e.g., loracarbef), cefixime, ceftriaxone, antipseudomonal(e.g, ceftazidime, cefoperazone), cefdinir, cefcapene, cefdaloxime,ceftizoxime, cefmenoxime, cefotaxime, cefpiramide, cefpodoxime,ceftibuten, cefditoren, cefetamet, cefodizime, cefpimizole, cefsulodin,cefteram, ceftiolene, oxacephem (e.g., flomoxef, latamoxef), cefepime,cefozopran, cefpirome, cefquinome, ceftaroline fosamil, ceftolozane,ceftobiprole, ceftiofur, cefquinome, cefovecin, a pharmaceuticallyacceptable salt thereof, a prodrug thereof, an analog thereof, or aderivative thereof.

In some embodiments, the compound is a thiopenem.

In some embodiments, the compound is of Formula (I):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R¹ is H or optionallysubstituted alkyl.

In some embodiments, the compound is of Formula (Ia):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the compound is of Formula (Ib):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, R¹ is H.

In some embodiments, the compound is of Formula (II):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the compound is of Formula (IIa):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, the compound is of Formula (IIb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof.

In some embodiments, R¹ is optionally substituted alkyl.

In some embodiments, the compound is of any one of Formulae (III),(IIIa), and (IIIb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R² is H or optionallysubstituted alkyl.

In some embodiments, the compound is selected from the group consistingof:

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof.

In some embodiments, the compound is selected from the group consistingof:

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof.

In some embodiments, the compound is of any one of Formulae (IV), (IVa),and (IVb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R³ is H or optionallysubstituted alkyl.

In some embodiments, R³ is C₂-C₈ alkyl.

In some embodiments, R³ is CH₂CH₃, CH₂CH₂CH₃, or CH₂CH(CH₃)₂.

Definitions

As used herein, “alkyl”, “C₁, C₂, C₃, C₄, C₅ or C₆ alkyl” or “C₁-C₆alkyl” is intended to include C₁, C₂, C₃, C₄, C₅ or C₆ straight chain(linear) saturated aliphatic hydrocarbon groups and C₃, C₄, C₅ or C₆branched saturated aliphatic hydrocarbon groups. For example, C₁-C₆alkyl is intended to include C₁, C₂, C₃, C₄, C₅ and C₆ alkyl groups.Examples of alkyl include, moieties having from one to six carbon atoms,such as, but not limited to, methyl, ethyl, n-propyl, i-propyl, n-butyl,s-butyl, t-butyl, n-pentyl, s-pentyl or n-hexyl. In certain embodiments,a straight chain or branched alkyl has six or fewer carbon atoms (e.g.,C₁-C₆ for straight chain, C₃-C₆ for branched chain), and in anotherembodiment, a straight chain or branched alkyl has four or fewer carbonatoms.

As used herein, the term “cycloalkyl” refers to a saturated orunsaturated nonaromatic hydrocarbon mono- or multi-ring (e.g., fused,bridged, or spiro rings) system having 3 to 30 carbon atoms (e.g.,C₃-C₁₂, C₃-C₁₀, or C₃-C₈). Examples of cycloalkyl include, but are notlimited to, cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl,cycloheptyl, cyclooctyl, cyclopentenyl, cyclohexenyl, cycloheptenyl,1,2,3,4-tetrahydronaphthalenyl, and adamantyl.

As used herein, the term “heterocycloalkyl” refers to a saturated orunsaturated nonaromatic 3-8 membered monocyclic, 7-12 membered bicyclic(fused, bridged, or spiro rings), or 11-14 membered tricyclic ringsystem (fused, bridged, or spiro rings) having one or more heteroatoms(such as O, N, S, P, or Se), e.g., 1 or 1-2 or 1-3 or 1-4 or 1-5 or 1-6heteroatoms, or e.g., 1, 2, 3, 4, 5, or 6 heteroatoms, independentlyselected from the group consisting of nitrogen, oxygen and sulfur,unless specified otherwise. Examples of heterocycloalkyl groups include,but are not limited to, piperidinyl, piperazinyl, pyrrolidinyl,dioxanyl, tetrahydrofuranyl, isoindolinyl, indolinyl, imidazolidinyl,pyrazolidinyl, oxazolidinyl, isoxazolidinyl, triazolidinyl, oxiranyl,azetidinyl, oxetanyl, thietanyl, 1,2,3,6-tetrahydropyridinyl,tetrahydropyranyl, dihydropyranyl, pyranyl, morpholinyl,tetrahydrothiopyranyl, 1,4-diazepanyl, 1,4-oxazepanyl,2-oxa-5-azabicyclo[2.2.1]heptanyl, 2,5-diazabicyclo[2.2.1]heptanyl,2-oxa-6-azaspiro[3.3]heptanyl, 2,6-diazaspiro[3.3]heptanyl,1,4-dioxa-8-azaspiro[4.5]decanyl, 1,4-dioxaspiro[4.5]decanyl,1-oxaspiro[4.5]decanyl, 1-azaspiro[4.5]decanyl,3′H-spiro[cyclohexane-1,1′-isobenzofuran]-yl,7′H-spiro[cyclohexane-1,5′-furo[3,4-b]pyridin]-yl,3′H-spiro[cyclohexane-1,1′-furo[3,4-c]pyridin]-yl,3-azabicyclo[3.1.0]hexanyl, 3-azabicyclo[3.1.0]hexan-3-yl,1,4,5,6-tetrahydropyrrolo[3,4-c]pyrazolyl,3,4,5,6,7,8-hexahydropyrido[4,3-d]pyrimidinyl,4,5,6,7-tetrahydro-1H-pyrazolo[3,4-c]pyridinyl,5,6,7,8-tetrahydropyrido[4,3-d]pyrimidinyl, 2-azaspiro[3.3]heptanyl,2-methyl-2-azaspiro[3.3]heptanyl, 2-azaspiro[3.5]nonanyl,2-methyl-2-azaspiro[3.5]nonanyl, 2-azaspiro[4.5]decanyl,2-methyl-2-azaspiro[4.5]decanyl, 2-oxa-azaspiro[3.4]octanyl,2-oxa-azaspiro[3.4]octan-6-yl, and the like. In the case of multicyclicnon-aromatic rings, only one of the rings needs to be non-aromatic(e.g., 1,2,3,4-tetrahydronaphthalenyl or 2,3-dihydroindole).

As used herein, the term “optionally substituted alkyl” refers tounsubstituted alkyl or alkyl having designated substituents replacingone or more hydrogen atoms on one or more carbons of the hydrocarbonbackbone. Such substituents can include, for example, alkyl, alkenyl,alkynyl, halogen, hydroxyl, alkylcarbonyloxy, arylcarbonyloxy,alkoxycarbonyloxy, aryloxycarbonyloxy, carboxylate, alkylcarbonyl,arylcarbonyl, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl,dialkylaminocarbonyl, alkylthiocarbonyl, alkoxyl, phosphate,phosphonato, phosphinato, amino (including alkylamino, dialkylamino,arylamino, diarylamino and alkylarylamino), acylamino (includingalkylcarbonylamino, arylcarbonylamino, carbamoyl and ureido), amidino,imino, sulfhydryl, alkylthio, arylthio, thiocarboxylate, sulfates,alkylsulfinyl, sulfonato, sulfamoyl, sulfonamido, nitro,trifluoromethyl, cyano, azido, heterocyclyl, alkylaryl, or an aromaticor heteroaromatic moiety.

As used herein, the term “alkenyl” includes unsaturated aliphatic groupsanalogous in length and possible substitution to the alkyls describedabove, but that contain at least one double bond. For example, the term“alkenyl” includes straight chain alkenyl groups (e.g., ethenyl,propenyl, butenyl, pentenyl, hexenyl, heptenyl, octenyl, nonenyl,decenyl), and branched alkenyl groups. In certain embodiments, astraight chain or branched alkenyl group has six or fewer carbon atomsin its backbone (e.g., C₂-C₆ for straight chain, C₃-C₆ for branchedchain). The term “C₂-C₆” includes alkenyl groups containing two to sixcarbon atoms. The term “C₃-C₆” includes alkenyl groups containing threeto six carbon atoms.

As used herein, the term “alkynyl” includes unsaturated aliphatic groupsanalogous in length and possible substitution to the alkyls describedabove, but which contain at least one triple bond. For example,“alkynyl” includes straight chain alkynyl groups (e.g., ethynyl,propynyl, butynyl, pentynyl, hexynyl, heptynyl, octynyl, nonynyl,decynyl), and branched alkynyl groups. In certain embodiments, astraight chain or branched alkynyl group has six or fewer carbon atomsin its backbone (e.g., C₂-C₆ for straight chain, C₃-C₆ for branchedchain). The term “C₂-C₆” includes alkynyl groups containing two to sixcarbon atoms. The term “C₃-C₆” includes alkynyl groups containing threeto six carbon atoms. As used herein, “C₂-C₆ alkenylene linker” or “C₂-C₆alkynylene linker” is intended to include C₂, C₃, C₄, C₅ or C₆ chain(linear or branched) divalent unsaturated aliphatic hydrocarbon groups.For example, C₂-C₆ alkenylene linker is intended to include C₂, C₃, C₄,C₅ and C₆ alkenylene linker groups.

Other optionally substituted moieties (such as optionally substitutedcycloalkyl, heterocycloalkyl, aryl, or heteroaryl) include both theunsubstituted moieties and the moieties having one or more of thedesignated substituents. For example, substituted heterocycloalkylincludes those substituted with one or more alkyl groups, such as2,2,6,6-tetramethyl-piperidinyl and2,2,6,6-tetramethyl-1,2,3,6-tetrahydropyridinyl.

As used herein, the term “aryl” includes groups with aromaticity,including “conjugated,” or multicyclic systems with one or more aromaticrings and do not contain any heteroatom in the ring structure. Examplesinclude phenyl, naphthalenyl, etc.

As used herein, the term “heteroaryl” is intended to include a stable5-, 6-, or 7-membered monocyclic or 7-, 8-, 9-, 10-, 11- or 12-memberedbicyclic aromatic heterocyclic ring which consists of carbon atoms andone or more heteroatoms, e.g., 1 or 1-2 or 1-3 or 1-4 or 1-5 or 1-6heteroatoms, or e.g., 1, 2, 3, 4, 5, or 6 heteroatoms, independentlyselected from the group consisting of nitrogen, oxygen and sulfur. Thenitrogen atom may be substituted or unsubstituted (i.e., N or NR whereinR is H or other substituents, as defined). The nitrogen and sulfurheteroatoms may optionally be oxidized (i.e., N→O and S(O)_(p), wherep=1 or 2). It is to be noted that total number of S and O atoms in thearomatic heterocycle is not more than 1. Examples of heteroaryl groupsinclude pyrrole, furan, thiophene, thiazole, isothiazole, imidazole,triazole, tetrazole, pyrazole, oxazole, isoxazole, pyridine, pyrazine,pyridazine, pyrimidine, and the like.

Furthermore, the terms “aryl” and “heteroaryl” include multicyclic aryland heteroaryl groups, e.g., tricyclic, bicyclic, e.g., naphthalene,benzoxazole, benzodioxazole, benzothiazole, benzoimidazole,benzothiophene, quinoline, isoquinoline, naphthrydine, indole,benzofuran, purine, benzofuran, deazapurine, indolizine.

The cycloalkyl, heterocycloalkyl, aryl, or heteroaryl ring can besubstituted at one or more ring positions (e.g., the ring-forming carbonor heteroatom such as N) with such substituents as described above, forexample, alkyl, alkenyl, alkynyl, halogen, hydroxyl, alkoxy,alkylcarbonyloxy, arylcarbonyloxy, alkoxycarbonyloxy,aryloxycarbonyloxy, carboxylate, alkylcarbonyl, alkylaminocarbonyl,aralkylaminocarbonyl, alkenylaminocarbonyl, alkylcarbonyl, arylcarbonyl,aralkylcarbonyl, alkenylcarbonyl, alkoxycarbonyl, aminocarbonyl,alkylthiocarbonyl, phosphate, phosphonato, phosphinato, amino (includingalkylamino, dialkylamino, arylamino, diarylamino and alkylarylamino),acylamino (including alkylcarbonylamino, arylcarbonylamino, carbamoyland ureido), amidino, imino, sulfhydryl, alkylthio, arylthio,thiocarboxylate, sulfates, alkylsulfinyl, sulfonato, sulfamoyl,sulfonamido, nitro, trifluoromethyl, cyano, azido, heterocyclyl,alkylaryl, or an aromatic or heteroaromatic moiety. Aryl and heteroarylgroups can also be fused or bridged with alicyclic or heterocyclicrings, which are not aromatic so as to form a multicyclic system (e.g.,tetralin, methylenedioxyphenyl such as benzo[d][1,3]dioxole-5-yl).

As used herein, the term “carbocycle” or “carbocyclic ring” is intendedto include any stable monocyclic, bicyclic or tricyclic ring having thespecified number of carbons, any of which may be saturated, unsaturated,or aromatic. Carbocycle includes cycloalkyl and aryl. For example, aC₃-C₁₄ carbocycle is intended to include a monocyclic, bicyclic ortricyclic ring having 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 or 14 carbonatoms. Examples of carbocycles include, but are not limited to,cyclopropyl, cyclobutyl, cyclobutenyl, cyclopentyl, cyclopentenyl,cyclohexyl, cycloheptenyl, cycloheptyl, cycloheptenyl, adamantyl,cyclooctyl, cyclooctenyl, cyclooctadienyl, fluorenyl, phenyl, naphthyl,indanyl, adamantyl and tetrahydronaphthyl. Bridged rings are alsoincluded in the definition of carbocycle, including, for example,[3.3.0]bicyclooctane, [4.3.0]bicyclononane, and [4.4.0] bicyclodecaneand [2.2.2] bicyclooctane. A bridged ring occurs when one or more carbonatoms link two non-adjacent carbon atoms. In one embodiment, bridgerings are one or two carbon atoms. It is noted that a bridge alwaysconverts a monocyclic ring into a tricyclic ring. When a ring isbridged, the substituents recited for the ring may also be present onthe bridge. Fused (e.g., naphthyl, tetrahydronaphthyl) and spiro ringsare also included.

As used herein, the term “heterocycle” or “heterocyclic group” includesany ring structure (saturated, unsaturated, or aromatic) which containsat least one ring heteroatom (e.g., 1-4 heteroatoms selected from N, Oand S). Heterocycle includes heterocycloalkyl and heteroaryl.

Examples of heterocycles include, but are not limited to, morpholine,pyrrolidine, tetrahydrothiophene, piperidine, piperazine, oxetane,pyran, tetrahydropyran, azetidine, and tetrahydrofuran.

Examples of heterocyclic groups include, but are not limited to,acridinyl, azocinyl, benzimidazolyl, benzofuranyl, benzothiofuranyl,benzothiophenyl, benzoxazolyl, benzoxazolinyl, benzthiazolyl,benztriazolyl, benztetrazolyl, benzisoxazolyl, benzisothiazolyl,benzimidazolinyl, carbazolyl, 4aH-carbazolyl, carbolinyl, chromanyl,chromenyl, cinnolinyl, decahydroquinolinyl, 2H,6H-1,5,2-dithiazinyl,dihydrofuro[2,3-b]tetrahydrofuran, furanyl, furazanyl, imidazolidinyl,imidazolinyl, imidazolyl, 1H-indazolyl, indolenyl, indolinyl,indolizinyl, indolyl, 3H-indolyl, isatinoyl, isobenzofuranyl,isochromanyl, isoindazolyl, isoindolinyl, isoindolyl, isoquinolinyl,isothiazolyl, isoxazolyl, methylenedioxyphenyl (e.g.,benzo[d][1,3]dioxole-5-yl), morpholinyl, naphthyridinyl,octahydroisoquinolinyl, oxadiazolyl, 1,2,3-oxadiazolyl,1,2,4-oxadiazolyl, 1,2,5-oxadiazolyl, 1,3,4-oxadiazolyl,1,2,4-oxadiazol5(4H)-one, oxazolidinyl, oxazolyl, oxindolyl,pyrimidinyl, phenanthridinyl, phenanthrolinyl, phenazinyl,phenothiazinyl, phenoxathinyl, phenoxazinyl, phthalazinyl, piperazinyl,piperidinyl, piperidonyl, 4-piperidonyl, piperonyl, pteridinyl, purinyl,pyranyl, pyrazinyl, pyrazolidinyl, pyrazolinyl, pyrazolyl, pyridazinyl,pyridooxazole, pyridoimidazole, pyridothiazole, pyridinyl, pyridyl,pyrimidinyl, pyrrolidinyl, pyrrolinyl, 2H-pyrrolyl, pyrrolyl,quinazolinyl, quinolinyl, 4H-quinolizinyl, quinoxalinyl, quinuclidinyl,tetrahydrofuranyl, tetrahydroisoquinolinyl, tetrahydroquinolinyl,tetrazolyl, 6H-1,2,5-thiadiazinyl, 1,2,3-thiadiazolyl,1,2,4-thiadiazolyl, 1,2,5-thiadiazolyl, 1,3,4-thiadiazolyl,thianthrenyl, thiazolyl, thienyl, thienothiazolyl, thienooxazolyl,thienoimidazolyl, thiophenyl, triazinyl, 1,2,3-triazolyl,1,2,4-triazolyl, 1,2,5-triazolyl, 1,3,4-triazolyl and xanthenyl.

As used herein, the term “substituted,” means that any one or morehydrogen atoms on the designated atom is replaced with a selection fromthe indicated groups, provided that the designated atom's normal valencyis not exceeded, and that the substitution results in a stable compound.When a substituent is oxo or keto (i.e., ═O), then 2 hydrogen atoms onthe atom are replaced. Keto substituents are not present on aromaticmoieties. Ring double bonds, as used herein, are double bonds that areformed between two adjacent ring atoms (e.g., C═C, C═N or N═N). “Stablecompound” and “stable structure” are meant to indicate a compound thatis sufficiently robust to survive isolation to a useful degree of purityfrom a reaction mixture, and formulation into an efficacious therapeuticagent.

When a bond to a substituent is shown to cross a bond connecting twoatoms in a ring, then such substituent may be bonded to any atom in thering. When a substituent is listed without indicating the atom via whichsuch substituent is bonded to the rest of the compound of a givenformula, then such substituent may be bonded via any atom in suchformula. Combinations of substituents and/or variables are permissible,but only if such combinations result in stable compounds.

When any variable (e.g., R) occurs more than one time in any constituentor formula for a compound, its definition at each occurrence isindependent of its definition at every other occurrence. Thus, forexample, if a group is shown to be substituted with 0-2 R moieties, thenthe group may optionally be substituted with up to two R moieties and Rat each occurrence is selected independently from the definition of R.Also, combinations of substituents and/or variables are permissible, butonly if such combinations result in stable compounds.

As used herein, the term “hydroxy” or “hydroxyl” includes groups with an—OH or —O⁻.

As used herein, the term “halo” or “halogen” refers to fluoro, chloro,bromo and iodo. The term “perhalogenated” generally refers to a moietywherein all hydrogen atoms are replaced by halogen atoms. The term“haloalkyl” or “haloalkoxyl” refers to an alkyl or alkoxyl substitutedwith one or more halogen atoms.

As used herein, the term “carbonyl” includes compounds and moietieswhich contain a carbon connected with a double bond to an oxygen atom.Examples of moieties containing a carbonyl include, but are not limitedto, aldehydes, ketones, carboxylic acids, amides, esters, anhydrides,etc.

As used herein, the term “carboxyl” refers to —COOH or its C₁-C₆ alkylester.

As used herein, the term “acyl” includes moieties that contain the acylradical (R—C(O)—) or a carbonyl group. As used herein, the term“substituted acyl” includes acyl groups where one or more of thehydrogen atoms are replaced by, for example, alkyl groups, alkynylgroups, halogen, hydroxyl, alkylcarbonyloxy, arylcarbonyloxy,alkoxycarbonyloxy, aryloxycarbonyloxy, carboxylate, alkylcarbonyl,arylcarbonyl, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl,dialkylaminocarbonyl, alkylthiocarbonyl, alkoxyl, phosphate,phosphonato, phosphinato, amino (including alkylamino, dialkylamino,arylamino, diarylamino and alkylarylamino), acylamino (includingalkylcarbonylamino, arylcarbonylamino, carbamoyl and ureido), amidino,imino, sulfhydryl, alkylthio, arylthio, thiocarboxylate, sulfates,alkylsulfinyl, sulfonato, sulfamoyl, sulfonamido, nitro,trifluoromethyl, cyano, azido, heterocyclyl, alkylaryl, or an aromaticor heteroaromatic moiety.

As used herein, the term “alkoxy” or “alkoxyl” includes substituted andunsubstituted alkyl, alkenyl and alkynyl groups covalently linked to anoxygen atom. Examples of alkoxy groups or alkoxyl radicals include, butare not limited to, methoxy, ethoxy, isopropyloxy, propoxy, butoxy andpentoxy groups. Examples of substituted alkoxy groups includehalogenated alkoxy groups. The alkoxy groups can be substituted withgroups such as alkenyl, alkynyl, halogen, hydroxyl, alkylcarbonyloxy,arylcarbonyloxy, alkoxycarbonyloxy, aryloxycarbonyloxy, carboxylate,alkylcarbonyl, arylcarbonyl, alkoxycarbonyl, aminocarbonyl,alkylaminocarbonyl, dialkylaminocarbonyl, alkylthiocarbonyl, alkoxyl,phosphate, phosphonato, phosphinato, amino (including alkylamino,dialkylamino, arylamino, diarylamino, and alkylarylamino), acylamino(including alkylcarbonylamino, arylcarbonylamino, carbamoyl and ureido),amidino, imino, sulfhydryl, alkylthio, arylthio, thiocarboxylate,sulfates, alkylsulfinyl, sulfonato, sulfamoyl, sulfonamido, nitro,trifluoromethyl, cyano, azido, heterocyclyl, alkylaryl, or an aromaticor heteroaromatic moieties. Examples of halogen substituted alkoxygroups include, but are not limited to, fluoromethoxy, difluoromethoxy,trifluoromethoxy, chloromethoxy, dichloromethoxy and trichloromethoxy.

As used herein, the term “ether” or “alkoxy” includes compounds ormoieties which contain an oxygen bonded to two carbon atoms orheteroatoms. For example, the term includes “alkoxyalkyl,” which refersto an alkyl, alkenyl, or alkynyl group covalently bonded to an oxygenatom which is covalently bonded to an alkyl group.

As used herein, the term “ester” includes compounds or moieties whichcontain a carbon or a heteroatom bound to an oxygen atom which is bondedto the carbon of a carbonyl group. The term “ester” includesalkoxycarboxy groups such as methoxycarbonyl, ethoxycarbonyl,propoxycarbonyl, butoxycarbonyl, pentoxycarbonyl, etc.

As used herein, the term “thioalkyl” includes compounds or moietieswhich contain an alkyl group connected with a sulfur atom. The thioalkylgroups can be substituted with groups such as alkyl, alkenyl, alkynyl,halogen, hydroxyl, alkylcarbonyloxy, arylcarbonyloxy, alkoxycarbonyloxy,aryloxycarbonyloxy, carboxylate, carboxyacid, alkylcarbonyl,arylcarbonyl, alkoxycarbonyl, aminocarbonyl, alkylaminocarbonyl,dialkylaminocarbonyl, alkylthiocarbonyl, alkoxyl, amino (includingalkylamino, dialkylamino, arylamino, diarylamino and alkylarylamino),acylamino (including alkylcarbonylamino, arylcarbonylamino, carbamoyland ureido), amidino, imino, sulfhydryl, alkylthio, arylthio,thiocarboxylate, sulfates, alkylsulfinyl, sulfonato, sulfamoyl,sulfonamido, nitro, trifluoromethyl, cyano, azido, heterocyclyl,alkylaryl, or an aromatic or heteroaromatic moieties.

As used herein, the term “thiocarbonyl” or “thiocarboxy” includescompounds and moieties which contain a carbon connected with a doublebond to a sulfur atom.

As used herein, the term “thioether” includes moieties which contain asulfur atom bonded to two carbon atoms or heteroatoms. Examples ofthioethers include, but are not limited to alkthioalkyls,alkthioalkenyls, and alkthioalkynyls. The term “alkthioalkyls” includemoieties with an alkyl, alkenyl, or alkynyl group bonded to a sulfuratom which is bonded to an alkyl group. Similarly, the term“alkthioalkenyls” refers to moieties wherein an alkyl, alkenyl oralkynyl group is bonded to a sulfur atom which is covalently bonded toan alkenyl group; and alkthioalkynyls” refers to moieties wherein analkyl, alkenyl or alkynyl group is bonded to a sulfur atom which iscovalently bonded to an alkynyl group.

As used herein, the term “amine” or “amino” refers to —NH₂. “Alkylamino”includes groups of compounds wherein the nitrogen of —NH₂ is bound to atleast one alkyl group.

Examples of alkylamino groups include benzylamino, methylamino,ethylamino, phenethylamino, etc.

As used herein, the term “dialkylamino” includes groups wherein thenitrogen of —NH₂ is bound to two alkyl groups. Examples of dialkylaminogroups include, but are not limited to, dimethylamino and diethylamino.

As used herein, the terms “arylamino” and “diarylamino” include groupswherein the nitrogen is bound to at least one or two aryl groups,respectively.

As used herein, the terms “aminoaryl” and “aminoaryloxy” refer to aryland aryloxy substituted with amino.

As used herein, the terms “alkylarylamino,” “alkylaminoaryl” or“arylaminoalkyl” refers to an amino group which is bound to at least onealkyl group and at least one aryl group.

As used herein, the terms “alkaminoalkyl” refers to an alkyl, alkenyl,or alkynyl group bound to a nitrogen atom which is also bound to analkyl group.

As used herein, the terms “acylamino” includes groups wherein nitrogenis bound to an acyl group. Examples of acylamino include, but are notlimited to, alkylcarbonylamino, arylcarbonylamino, carbamoyl and ureidogroups.

As used herein, the term“amide” or “aminocarboxy” includes compounds ormoieties that contain a nitrogen atom that is bound to the carbon of acarbonyl or a thiocarbonyl group.

As used herein, the term “alkaminocarboxy” includes alkyl, alkenyl oralkynyl groups bound to an amino group which is bound to the carbon of acarbonyl or thiocarbonyl group.

As used herein, the term“arylaminocarboxy” includes aryl or heteroarylmoieties bound to an amino group that is bound to the carbon of acarbonyl or thiocarbonyl group.

As used herein, the terms “alkylaminocarboxy”, “alkenylaminocarboxy”,“alkynylaminocarboxy” and “arylaminocarboxy” include moieties whereinalkyl, alkenyl, alkynyl and aryl moieties, respectively, are bound to anitrogen atom which is in turn bound to the carbon of a carbonyl group.

Amides can be substituted with substituents such as straight chainalkyl, branched alkyl, cycloalkyl, aryl, heteroaryl or heterocycle.Substituents on amide groups may be further substituted.

It is understood that probenecid (e.g., sold under the brandnameProbalan) is of the following structure:

Compounds of the present disclosure that contain nitrogens can beconverted to N-oxides by treatment with an oxidizing agent (e.g.,3-chloroperoxybenzoic acid (mCPBA) and/or hydrogen peroxides) to affordother compounds of the present disclosure. Thus, all shown and claimednitrogen-containing compounds are considered, when allowed by valencyand structure, to include both the compound as shown and its N-oxidederivative (which can be designated as N→O or N⁺—O⁻). Furthermore, inother instances, the nitrogens in the compounds of the presentdisclosure can be converted to N-hydroxy or N-alkoxy compounds. Forexample, N-hydroxy compounds can be prepared by oxidation of the parentamine by an oxidizing agent such as m-CPBA. All shown and claimednitrogen-containing compounds are also considered, when allowed byvalency and structure, to cover both the compound as shown and itsN-hydroxy (i.e., N—OH) and N-alkoxy (i.e., N—OR, wherein R issubstituted or unsubstituted C₁-C₆ alkyl, C₁-C₆ alkenyl, C₁-C₆ alkynyl,3-14-membered carbocycle or 3-14-membered heterocycle) derivatives.

In the present specification, the structural formula of the compoundrepresents a certain isomer for convenience in some cases, but thepresent disclosure includes all isomers, such as geometrical isomers,optical isomers based on an asymmetrical carbon, stereoisomers,tautomers, and the like, it being understood that not all isomers mayhave the same level of activity. In addition, a crystal polymorphism maybe present for the compounds represented by the formula. It is notedthat any crystal form, crystal form mixture, or anhydride or hydratethereof is included in the scope of the present disclosure.

As used herein, the term “isomerism” means compounds that have identicalmolecular formulae but differ in the sequence of bonding of their atomsor in the arrangement of their atoms in space. Isomers that differ inthe arrangement of their atoms in space are termed “stereoisomers.”Stereoisomers that are not mirror images of one another are termed“diastereoisomers,” and stereoisomers that are non-superimposable mirrorimages of each other are termed “enantiomers” or sometimes opticalisomers. A mixture containing equal amounts of individual enantiomericforms of opposite chirality is termed a “racemic mixture.”

As used herein, the term “chiral center” refers to a carbon atom bondedto four nonidentical substituents.

As used herein, the term “chiral isomer” means a compound with at leastone chiral center. Compounds with more than one chiral center may existeither as an individual diastereomer or as a mixture of diastereomers,termed “diastereomeric mixture.” When one chiral center is present, astereoisomer may be characterized by the absolute configuration (R or S)of that chiral center. Absolute configuration refers to the arrangementin space of the substituents attached to the chiral center. Thesubstituents attached to the chiral center under consideration areranked in accordance with the Sequence Rule of Cahn, Ingold and Prelog.(Cahn et al., Angew. Chem. Inter. Edit. 1966, 5, 385; errata 511; Cahnet al., Angew. Chem. 1966, 78, 413; Cahn and Ingold, J. Chem. Soc. 1951(London), 612; Cahn et al., Erperientia 1956, 12, 81; Cahn, J. Chem.Educ. 1964, 41, 116).

As used herein, the term “geometric isomer” means the diastereomers thatowe their existence to hindered rotation about double bonds or acycloalkyl linker (e.g., 1,3-cylcobutyl). These configurations aredifferentiated in their names by the prefixes cis and trans, or Z and E,which indicate that the groups are on the same or opposite side of thedouble bond in the molecule according to the Cahn-Ingold-Prelog rules.

It is to be understood that the compounds of the present disclosure maybe depicted as different chiral isomers or geometric isomers. It is alsoto be understood that when compounds have chiral isomeric or geometricisomeric forms, all isomeric forms are intended to be included in thescope of the present disclosure, and the naming of the compounds doesnot exclude any isomeric forms, it being understood that not all isomersmay have the same level of activity.

It is to be understood that the structures and other compounds discussedin this disclosure include all atropic isomers thereof. It is also to beunderstood that not all atropic isomers may have the same level ofactivity.

As used herein, the term “atropic isomers” are a type of stereoisomer inwhich the atoms of two isomers are arranged differently in space.Atropic isomers owe their existence to a restricted rotation caused byhindrance of rotation of large groups about a central bond. Such atropicisomers typically exist as a mixture, however as a result of recentadvances in chromatography techniques, it has been possible to separatemixtures of two atropic isomers in select cases.

As used herein, the term “tautomer” is one of two or more structuralisomers that exist in equilibrium and is readily converted from oneisomeric form to another. This conversion results in the formalmigration of a hydrogen atom accompanied by a switch of adjacentconjugated double bonds. Tautomers exist as a mixture of a tautomericset in solution. In solutions where tautomerization is possible, achemical equilibrium of the tautomers will be reached. The exact ratioof the tautomers depends on several factors, including temperature,solvent and pH. The concept of tautomers that are interconvertible bytautomerizations is called tautomerism. Of the various types oftautomerism that are possible, two are commonly observed. In keto-enoltautomerism a simultaneous shift of electrons and a hydrogen atomoccurs. Ring-chain tautomerism arises as a result of the aldehyde group(—CHO) in a sugar chain molecule reacting with one of the hydroxy groups(—OH) in the same molecule to give it a cyclic (ring-shaped) form asexhibited by glucose.

It is to be understood that the compounds of the present disclosure maybe depicted as different tautomers. It should also be understood thatwhen compounds have tautomeric forms, all tautomeric forms are intendedto be included in the scope of the present disclosure, and the naming ofthe compounds does not exclude any tautomer form. It will be understoodthat certain tautomers may have a higher level of activity than others.

As used herein, the term “crystal polymorphs”, “polymorphs” or “crystalforms” means crystal structures in which a compound (or a salt orsolvate thereof) can crystallize in different crystal packingarrangements, all of which have the same elemental composition.Different crystal forms usually have different X-ray diffractionpatterns, infrared spectral, melting points, density hardness, crystalshape, optical and electrical properties, stability and solubility.Recrystallization solvent, rate of crystallization, storage temperature,and other factors may cause one crystal form to dominate. Crystalpolymorphs of the compounds can be prepared by crystallization underdifferent conditions.

It is to be understood that the compounds of any Formula describedherein include the compounds themselves, as well as their salts, andtheir solvates, if applicable. A salt, for example, can be formedbetween an anion and a positively charged group (e.g., amino) on asubstituted benzene compound. Suitable anions include chloride, bromide,iodide, sulfate, bisulfate, sulfamate, nitrate, phosphate, citrate,methanesulfonate, trifluoroacetate, glutamate, glucuronate, glutarate,malate, maleate, succinate, fumarate, tartrate, tosylate, salicylate,lactate, naphthalenesulfonate, and acetate (e.g., trifluoroacetate).

As used herein, the term “pharmaceutically acceptable anion” refers toan anion suitable for forming a pharmaceutically acceptable salt.Likewise, a salt can also be formed between a cation and a negativelycharged group (e.g., carboxylate) on a substituted benzene compound.

Suitable cations include sodium ion, potassium ion, magnesium ion,calcium ion, and an ammonium cation such as tetramethylammonium ion. Thesubstituted benzene compounds also include those salts containingquaternary nitrogen atoms.

It is to be understood that the compounds of the present disclosure, forexample, the salts of the compounds, can exist in either hydrated orunhydrated (the anhydrous) form or as solvates with other solventmolecules. Nonlimiting examples of hydrates include monohydrates,dihydrates, etc. Nonlimiting examples of solvates include ethanolsolvates, acetone solvates, etc.

As used herein, the term “solvate” means solvent addition forms thatcontain either stoichiometric or non-stoichiometric amounts of solvent.Some compounds have a tendency to trap a fixed molar ratio of solventmolecules in the crystalline solid state, thus forming a solvate. If thesolvent is water the solvate formed is a hydrate; and if the solvent isalcohol, the solvate formed is an alcoholate. Hydrates are formed by thecombination of one or more molecules of water with one molecule of thesubstance in which the water retains its molecular state as H₂O.

As used herein, the term “analog” refers to a chemical compound that isstructurally similar to another but differs slightly in composition (asin the replacement of one atom by an atom of a different element or inthe presence of a particular functional group, or the replacement of onefunctional group by another functional group). Thus, an analog is acompound that is similar or comparable in function and appearance, butnot in structure or origin to the reference compound.

As used herein, the term “derivative” refers to compounds that have acommon core structure, and are substituted with various groups asdescribed herein.

As used herein, the term “bioisostere” refers to a compound resultingfrom the exchange of an atom or of a group of atoms with another,broadly similar, atom or group of atoms. The objective of a bioisostericreplacement is to create a new compound with similar biologicalproperties to the parent compound. The bioisosteric replacement may bephysicochemically or topologically based. Examples of carboxylic acidbioisosteres include, but are not limited to, acyl sulfonimides,tetrazoles, sulfonates and phosphonates. See, e.g., Patani and LaVoie,Chem. Rev. 96, 3147-3176, 1996.

It is to be understood that the present disclosure is intended toinclude all isotopes of atoms occurring in the present compounds.Isotopes include those atoms having the same atomic number but differentmass numbers. By way of general example and without limitation, isotopesof hydrogen include tritium and deuterium, and isotopes of carboninclude C-13 and C-14.

As used herein, the expressions “one or more of A, B, or C,” “one ormore A, B, or C,” “one or more of A, B, and C,” “one or more A, B, andC,” “selected from the group consisting of A, B, and C”, “selected fromA, B, and C”, and the like are used interchangeably and all refer to aselection from a group consisting of A, B, and/or C, i.e., one or moreAs, one or more Bs, one or more Cs, or any combination thereof, unlessindicated otherwise.

It is to be understood that the present disclosure provides methods forthe synthesis of the compounds of any of the Formulae described herein.The present disclosure also provides detailed methods for the synthesisof various disclosed compounds of the present disclosure according tothe following schemes as well as those shown in the Examples.

It is to be understood that, throughout the description, wherecompositions are described as having, including, or comprising specificcomponents, it is contemplated that compositions also consistessentially of, or consist of, the recited components. Similarly, wheremethods or processes are described as having, including, or comprisingspecific process steps, the processes also consist essentially of, orconsist of, the recited processing steps. Further, it should beunderstood that the order of steps or order for performing certainactions is immaterial so long as the invention remains operable.Moreover, two or more steps or actions can be conducted simultaneously.

It is to be understood that the synthetic processes of the disclosurecan tolerate a wide variety of functional groups, therefore varioussubstituted starting materials can be used. The processes generallyprovide the desired final compound at or near the end of the overallprocess, although it may be desirable in certain instances to furtherconvert the compound to a pharmaceutically acceptable salt thereof.

It is to be understood that compounds of the present disclosure can beprepared in a variety of ways using commercially available startingmaterials, compounds known in the literature, or from readily preparedintermediates, by employing standard synthetic methods and procedureseither known to those skilled in the art, or which will be apparent tothe skilled artisan in light of the teachings herein. Standard syntheticmethods and procedures for the preparation of organic molecules andfunctional group transformations and manipulations can be obtained fromthe relevant scientific literature or from standard textbooks in thefield. Although not limited to any one or several sources, classic textssuch as Smith, M. B., March, J., March's Advanced Organic Chemistry:Reactions, Mechanisms, and Structure, 5^(th) edition, John Wiley & Sons:New York, 2001; Greene, T. W., Wuts, P. G. M., Protective Groups inOrganic Synthesis, 3^(rd) edition, John Wiley & Sons: New York, 1999; R.Larock, Comprehensive Organic Transformations, VCH Publishers (1989); L.Fieser and M. Fieser, Fieser and Fieser's Reagents for OrganicSynthesis, John Wiley and Sons (1994); and L. Paquette, ed.,Encyclopedia of Reagents for Organic Synthesis, John Wiley and Sons(1995), incorporated by reference herein, are useful and recognizedreference textbooks of organic synthesis known to those in the art

One of ordinary skill in the art will note that, during the reactionsequences and synthetic schemes described herein, the order of certainsteps may be changed, such as the introduction and removal of protectinggroups._One of ordinary skill in the art will recognize that certaingroups may require protection from the reaction conditions via the useof protecting groups. Protecting groups may also be used todifferentiate similar functional groups in molecules. A list ofprotecting groups and how to introduce and remove these groups can befound in Greene, T. W., Wuts, P. G. M., Protective Groups in OrganicSynthesis, 3^(rd) edition, John Wiley & Sons: New York, 1999.

It is to be understood that, unless otherwise stated, any description ofa method of treatment includes use of the compounds to provide suchtreatment or prophylaxis as is described herein, as well as use of thecompounds to prepare a medicament to treat or prevent such condition.The treatment includes treatment of human or non-human animals includingrodents and other disease models.

As used herein, the term “subject” is interchangeable with the term“subject in need thereof”, both of which refer to a subject having adisease or having an increased risk of developing the disease. A“subject” includes a mammal. The mammal can be e.g., a human orappropriate non-human mammal, such as primate, mouse, rat, dog, cat,cow, horse, goat, camel, sheep or a pig. The subject can also be a birdor fowl. In one embodiment, the mammal is a human.

As used herein, the term “comparable subject” refers to a subject withcomparable parameters, or in comparable conditions, as of the subjectbeing compared (e.g., the subject being treated). For example, the“comparable subject” may have a disease as of the subject beingcompared, or have an increased risk of developing the disease as of thesubject being compared. For another example, the “comparable subject”may exhibit one or more plasma pharmakinetic paramters (e.g., C_(max) orAUC) to one or more pharmaceutical agents (e.g., a β-lactam compound,probenecid, or a combination thereof) as of the subject being compared.In some embodiments, the “comparable subject” may be the subject beingcompared at a different time, e.g., the subject being treated (e.g., byadministrating a β-lactam compound and probenecid) may be subjected toconditions (e.g., administration of a β-lactam compound withoutprobenecid) as a “comparable subject” prior to the treatment.

As used herein, the term “candidate compound” refers to a compound ofthe present disclosure, or a pharmaceutically acceptable salt, polymorphor solvate thereof, that has been or will be tested in one or more invitro or in vivo biological assays, in order to determine if thatcompound is likely to elicit a desired biological or medical response ina cell, tissue, system, animal or human that is being sought by aresearcher or clinician. A candidate compound is a compound of thepresent disclosure, or a pharmaceutically acceptable salt, polymorph orsolvate thereof. The biological response or effect can occur in vitro orin an animal model, as well as other biological changes that areobservable in vitro. In vitro or in vivo biological assays can include,but are not limited to, enzymatic activity assays, electrophoreticmobility shift assays, reporter gene assays, in vitro cell viabilityassays, and the assays described herein.

As used herein, the term “treating” or “treat” describes the managementand care of a patient for the purpose of combating a disease, condition,or disorder and includes the administration of a compound of the presentdisclosure, or a pharmaceutically acceptable salt, polymorph or solvatethereof, to alleviate the symptoms or complications of a disease,condition or disorder, or to eliminate the disease, condition ordisorder. The term “treat” can also include treatment of a cell in vitroor an animal model.

As used herein, the term “temporal proximity” refers to thatadministration of one therapeutic agent (e.g., a β-lactam compounddisclosed herein) occurs within a time period before or after theadministration of another therapeutic agent (e.g., probenecid), suchthat the therapeutic effect of the one therapeutic agent overlaps withthe therapeutic effect of the other therapeutic agent. In someembodiments, the therapeutic effect of the one therapeutic agentcompletely overlaps with the therapeutic effect of the other therapeuticagent. In some embodiments, “temporal proximity” means thatadministration of one therapeutic agent occurs within a time periodbefore or after the administration of another therapeutic agent, suchthat there is a synergistic effect between the one therapeutic agent andthe other therapeutic agent. “Temporal proximity” may vary according tovarious factors, including but not limited to, the age, gender, weight,genetic background, medical condition, disease history, and treatmenthistory of the subject to which the therapeutic agents are to beadministered; the disease or condition to be treated or ameliorated; thetherapeutic outcome to be achieved; the dosage, dosing frequency, anddosing duration of the therapeutic agents; the pharmacokinetics andpharmacodynamics of the therapeutic agents; and the route(s) throughwhich the therapeutic agents are administered. In some embodiments,“temporal proximity” means within 15 minutes, within 30 minutes, withinan hour, within two hours, within four hours, within six hours, withineight hours, within 12 hours, within 18 hours, within 24 hours, within36 hours, within 2 days, within 3 days, within 4 days, within 5 days,within 6 days, within a week, within 2 weeks, within 3 weeks, within 4weeks, with 6 weeks, or within 8 weeks. In some embodiments, multipleadministration of one therapeutic agent can occur in temporal proximityto a single administration of another therapeutic agent. In someembodiments, temporal proximity may change during a treatment cycle orwithin a dosing regimen.

It is to be understood that a compound of the present disclosure, or apharmaceutically acceptable salt, polymorph or solvate thereof, can ormay also be used to prevent a relevant disease, condition or disorder,or used to identify suitable candidates for such purposes.

As used herein, the term “preventing,” “prevent,” or “protectingagainst” describes reducing or eliminating the onset of the symptoms orcomplications of such disease, condition or disorder.

It is to be understood that one skilled in the art may refer to generalreference texts for detailed descriptions of known techniques discussedherein or equivalent techniques. These texts include Ausubel et al.,Current Protocols in Molecular Biology, John Wiley and Sons, Inc.(2005); Sambrook et al., Molecular Cloning, A Laboratory Manual (3^(rd)edition), Cold Spring Harbor Press, Cold Spring Harbor, N.Y. (2000);Coligan et al., Current Protocols in Immunology, John Wiley & Sons,N.Y.; Enna et al., Current Protocols in Pharmacology, John Wiley & Sons,N.Y.; Fingl et al., The Pharmacological Basis of Therapeutics (1975),Remington's Pharmaceutical Sciences, Mack Publishing Co., Easton, Pa.,18^(th) edition (1990), Mandell, et al., Principles and Practice ofInfectious Diseases, Saunders Publishing (8th edition, 2014). Thesetexts can, of course, also be referred to in making or using an aspectof the disclosure.

As used herein, the term “combination therapy” or “co-therapy” includesthe administration of a compound of the present disclosure, or apharmaceutically acceptable salt, polymorph or solvate thereof, and atleast a second agent as part of a specific treatment regimen intended toprovide the beneficial effect from the co-action of these therapeuticagents. The beneficial effect of the combination includes, but is notlimited to, pharmacokinetic or pharmacodynamic co-action resulting fromthe combination of therapeutic agents.

It is to be understood that the present disclosure also providespharmaceutical compositions comprising any compound described herein incombination with at least one pharmaceutically acceptable excipient orcarrier.

As used herein, the term “pharmaceutical composition” is a formulationcontaining the compounds of the present disclosure in a form suitablefor administration to a subject. In one embodiment, the pharmaceuticalcomposition is in bulk or in unit dosage form. The unit dosage form isany of a variety of forms, including, for example, a capsule, an IV bag,a tablet, a single pump on an aerosol inhaler or a vial. The quantity ofactive ingredient (e.g., a formulation of the disclosed compound orsalt, hydrate, solvate or isomer thereof) in a unit dose of compositionis an effective amount and is varied according to the particulartreatment involved. One skilled in the art will appreciate that it issometimes necessary to make routine variations to the dosage dependingon the age and condition of the patient. The dosage will also depend onthe route of administration. A variety of routes are contemplated,including oral, pulmonary, rectal, parenteral, transdermal,subcutaneous, intravenous, intramuscular, intraperitoneal, inhalational,buccal, sublingual, intrapleural, intrathecal, intranasal, and the like.Dosage forms for the topical or transdermal administration of a compoundof this disclosure include powders, sprays, ointments, pastes, creams,lotions, gels, solutions, patches and inhalants. In one embodiment, theactive compound is mixed under sterile conditions with apharmaceutically acceptable carrier, and with any preservatives,buffers, or propellants that are required.

As used herein, the term “pharmaceutically acceptable” refers to thosecompounds, anions, cations, materials, compositions, carriers, and/ordosage forms which are, within the scope of sound medical judgment,suitable for use in contact with the tissues of human beings and animalswithout excessive toxicity, irritation, allergic response, or otherproblem or complication, commensurate with a reasonable benefit/riskratio.

As used herein, the term “pharmaceutically acceptable excipient” meansan excipient that is useful in preparing a pharmaceutical compositionthat is generally safe, non-toxic and neither biologically nor otherwiseundesirable, and includes excipient that is acceptable for veterinaryuse as well as human pharmaceutical use. A “pharmaceutically acceptableexcipient” as used in the specification and claims includes both one andmore than one such excipient.

It is to be understood that a pharmaceutical composition of thedisclosure is formulated to be compatible with its intended route ofadministration. Examples of routes of administration include parenteral,e.g., intravenous, intradermal, subcutaneous, oral (e.g., inhalation),transdermal (topical), and transmucosal administration. Solutions orsuspensions used for parenteral, intradermal, or subcutaneousapplication can include the following components: a sterile diluent suchas water for injection, saline solution, fixed oils, polyethyleneglycols, glycerine, propylene glycol or other synthetic solvents;antibacterial agents such as benzyl alcohol or methyl parabens;antioxidants such as ascorbic acid or sodium bisulfite; chelating agentssuch as ethylenediaminetetraacetic acid; buffers such as acetates,citrates or phosphates, and agents for the adjustment of tonicity suchas sodium chloride or dextrose. The pH can be adjusted with acids orbases, such as hydrochloric acid or sodium hydroxide. The parenteralpreparation can be enclosed in ampoules, disposable syringes or multipledose vials made of glass or plastic.

It is to be understood that a compound or pharmaceutical composition ofthe disclosure can be administered to a subject in many of thewell-known methods currently used for chemotherapeutic treatment. Forexample, a compound of the disclosure may be injected into the bloodstream or body cavities or taken orally or applied through the skin withpatches. The dose chosen should be sufficient to constitute effectivetreatment but not so high as to cause unacceptable side effects. Thestate of the disease condition and the health of the patient shouldpreferably be closely monitored during and for a reasonable period aftertreatment.

As used herein, the term “therapeutically effective amount”, refers toan amount of a pharmaceutical agent to treat, ameliorate, or prevent anidentified disease or condition, or to exhibit a detectable therapeuticor inhibitory effect. The effect can be detected by any assay methodknown in the art. The precise effective amount for a subject will dependupon the subject's body weight, size, and health; the nature and extentof the condition; and the therapeutic or combination of therapeuticsselected for administration. Therapeutically effective amounts for agiven situation can be determined by routine experimentation that iswithin the skill and judgment of the clinician.

It is to be understood that, for any compound, the therapeuticallyeffective amount can be estimated initially either in cell cultureassays, e.g., of neoplastic cells, or in animal models, usually rats,mice, rabbits, dogs, or pigs. The animal model may also be used todetermine the appropriate concentration range and route ofadministration. Such information can then be used to determine usefuldoses and routes for administration in humans. Therapeutic/prophylacticefficacy and toxicity may be determined by standard pharmaceuticalprocedures in cell cultures or experimental animals, e.g., ED₅₀ (thedose therapeutically effective in 50% of the population) and LD₅₀ (thedose lethal to 50% of the population). The dose ratio between toxic andtherapeutic effects is the therapeutic index, and it can be expressed asthe ratio, LD₅₀/ED₅₀. Pharmaceutical compositions that exhibit largetherapeutic indices are preferred. The dosage may vary within this rangedepending upon the dosage form employed, sensitivity of the patient, andthe route of administration.

Dosage and administration are adjusted to provide sufficient levels ofthe active agent(s) or to maintain the desired effect. Factors which maybe taken into account include the severity of the disease state, generalhealth of the subject, age, weight, and gender of the subject, diet,time and frequency of administration, drug combination(s), reactionsensitivities, and tolerance/response to therapy. Long-actingpharmaceutical compositions may be administered every 3 to 4 days, everyweek, or once every two weeks depending on half-life and clearance rateof the particular formulation.

The pharmaceutical compositions containing active compounds of thepresent disclosure may be manufactured in a manner that is generallyknown, e.g., by means of conventional mixing, dissolving, granulating,dragee-making, levigating, emulsifying, encapsulating, entrapping, orlyophilizing processes. Pharmaceutical compositions may be formulated ina conventional manner using one or more pharmaceutically acceptablecarriers comprising excipients and/or auxiliaries that facilitateprocessing of the active compounds into preparations that can be usedpharmaceutically. Of course, the appropriate formulation is dependentupon the route of administration chosen.

Pharmaceutical compositions suitable for injectable use include sterileaqueous solutions (where water soluble) or dispersions and sterilepowders for the extemporaneous preparation of sterile injectablesolutions or dispersion. For intravenous administration, suitablecarriers include physiological saline, bacteriostatic water, CremophorEL™ (BASF, Parsippany, N.J.) or phosphate buffered saline (PBS). In allcases, the composition must be sterile and should be fluid to the extentthat easy syringeability exists. It must be stable under the conditionsof manufacture and storage and must be preserved against thecontaminating action of microorganisms such as bacteria and fungi. Thecarrier can be a solvent or dispersion medium containing, for example,water, ethanol, polyol (for example, glycerol, propylene glycol, andliquid polyethylene glycol, and the like), and suitable mixturesthereof. The proper fluidity can be maintained, for example, by the useof a coating such as lecithin, by the maintenance of the requiredparticle size in the case of dispersion and by the use of surfactants.Prevention of the action of microorganisms can be achieved by variousantibacterial and antifungal agents, for example, parabens,chlorobutanol, phenol, ascorbic acid, thimerosal, and the like. In manycases, it will be preferable to include isotonic agents, for example,sugars, polyalcohols such as mannitol and sorbitol, and sodium chloridein the composition. Prolonged absorption of the injectable compositionscan be brought about by including in the composition an agent whichdelays absorption, for example, aluminum monostearate and gelatin.

Sterile injectable solutions can be prepared by incorporating the activecompound in the required amount in an appropriate solvent with one or acombination of ingredients enumerated above, as required, followed byfiltered sterilization. Generally, dispersions are prepared byincorporating the active compound into a sterile vehicle that contains abasic dispersion medium and the required other ingredients from thoseenumerated above. In the case of sterile powders for the preparation ofsterile injectable solutions, methods of preparation are vacuum dryingand freeze-drying that yields a powder of the active ingredient plus anyadditional desired ingredient from a previously sterile-filteredsolution thereof.

Oral compositions generally include an inert diluent or an ediblepharmaceutically acceptable carrier. They can be enclosed in gelatincapsules or compressed into tablets. For the purpose of oral therapeuticadministration, the active compound can be incorporated with excipientsand used in the form of tablets, troches, or capsules. Oral compositionscan also be prepared using a fluid carrier for use as a mouthwash,wherein the compound in the fluid carrier is applied orally and swishedand expectorated or swallowed. Pharmaceutically compatible bindingagents, and/or adjuvant materials can be included as part of thecomposition. The tablets, pills, capsules, troches and the like cancontain any of the following ingredients, or compounds of a similarnature: a binder such as microcrystalline cellulose, gum tragacanth orgelatin; an excipient such as starch or lactose, a disintegrating agentsuch as alginic acid, Primogel, or corn starch; a lubricant such asmagnesium stearate or Sterotes; a glidant such as colloidal silicondioxide; a sweetening agent such as sucrose or saccharin; or a flavoringagent such as peppermint, methyl salicylate, or orange flavoring.

For administration by inhalation, the compounds are delivered in theform of an aerosol spray from pressured container or dispenser, whichcontains a suitable propellant, e.g., a gas such as carbon dioxide, or anebulizer.

Systemic administration can also be by transmucosal or transdermalmeans. For transmucosal or transdermal administration, penetrantsappropriate to the barrier to be permeated are used in the formulation.Such penetrants are generally known in the art, and include, forexample, for transmucosal administration, detergents, bile salts, andfusidic acid derivatives.

Transmucosal administration can be accomplished through the use of nasalsprays or suppositories. For transdermal administration, the activecompounds are formulated into ointments, salves, gels, or creams asgenerally known in the art.

The active compounds can be prepared with pharmaceutically acceptablecarriers that will protect the compound against rapid elimination fromthe body, such as a controlled release formulation, including implantsand microencapsulated delivery systems. Biodegradable, biocompatiblepolymers can be used, such as ethylene vinyl acetate, polyanhydrides,polyglycolic acid, collagen, polyorthoesters, and polylactic acid.Methods for preparation of such formulations will be apparent to thoseskilled in the art. The materials can also be obtained commercially fromAlza Corporation and Nova Pharmaceuticals, Inc. Liposomal suspensions(including liposomes targeted to infected cells with monoclonalantibodies to viral antigens) can also be used as pharmaceuticallyacceptable carriers. These can be prepared according to methods known tothose skilled in the art, for example, as described in U.S. Pat. No.4,522,811.

It is especially advantageous to formulate oral or parenteralcompositions in dosage unit form for ease of administration anduniformity of dosage. Dosage unit form as used herein refers tophysically discrete units suited as unitary dosages for the subject tobe treated; each unit containing a predetermined quantity of activecompound calculated to produce the desired therapeutic effect inassociation with the required pharmaceutical carrier. The specificationfor the dosage unit forms of the disclosure are dictated by and directlydependent on the unique characteristics of the active compound and theparticular therapeutic effect to be achieved.

In therapeutic applications, the dosages of the pharmaceuticalcompositions used in accordance with the disclosure vary depending onthe agent, the age, weight, and clinical condition of the recipientpatient, and the experience and judgment of the clinician orpractitioner administering the therapy, among other factors affectingthe selected dosage. Generally, the dose should be sufficient to resultin slowing, and preferably regressing, the symptoms of the disease andalso preferably causing complete regression of the disease. Dosages canrange from about 0.01 mg/kg per day to about 5000 mg/kg per day. Inpreferred aspects, dosages can range from about 1 mg/kg per day to about1000 mg/kg per day. In an aspect, the dose will be in the range of about0.1 mg/day to about 50 g/day; about 0.1 mg/day to about 25 g/day; about0.1 mg/day to about 10 g/day; about 0.1 mg to about 3 g/day; or about0.1 mg to about 1 g/day, in single, divided, or continuous doses (whichdose may be adjusted for the patient's weight in kg, body surface areain m², and age in years). An effective amount of a pharmaceutical agentis that which provides an objectively identifiable improvement as notedby the clinician or other qualified observer. Improvement in survivaland growth indicates regression. As used herein, the term “dosageeffective manner” refers to amount of an active compound to produce thedesired biological effect in a subject or cell.

It is to be understood that the pharmaceutical compositions can beincluded in a container, pack, or dispenser together with instructionsfor administration.

It is to be understood that, for the compounds of the present disclosurebeing capable of further forming salts, all of these forms are alsocontemplated within the scope of the claimed disclosure.

As used herein, the term “pharmaceutically acceptable salts” refer toderivatives of the compounds of the present disclosure wherein theparent compound is modified by making acid or base salts thereof. Insome embodiments, the pharmaceutically acceptable salt of a compound(e.g., a β-lactam compound or probenecid described herein) is also aprodrug of the compound. Examples of pharmaceutically acceptable saltsinclude, but are not limited to, mineral or organic acid salts of basicresidues such as amines, alkali or organic salts of acidic residues suchas carboxylic acids, and the like. The pharmaceutically acceptable saltsinclude the conventional non-toxic salts or the quaternary ammoniumsalts of the parent compound formed, for example, from non-toxicinorganic or organic acids. For example, such conventional non-toxicsalts include, but are not limited to, those derived from inorganic andorganic acids selected from 2-acetoxybenzoic, 2-hydroxyethane sulfonic,acetic, ascorbic, benzene sulfonic, benzoic, bicarbonic, carbonic,citric, edetic, ethane disulfonic, 1,2-ethane sulfonic, fumaric,glucoheptonic, gluconic, glutamic, glycolic, glycollyarsanilic,hexylresorcinic, hydrabamic, hydrobromic, hydrochloric, hydroiodic,hydroxymaleic, hydroxynaphthoic, isethionic, lactic, lactobionic, laurylsulfonic, maleic, malic, mandelic, methane sulfonic, napsylic, nitric,oxalic, pamoic, pantothenic, phenylacetic, phosphoric, polygalacturonic,propionic, salicylic, stearic, subacetic, succinic, sulfamic,sulfanilic, sulfuric, tannic, tartaric, toluene sulfonic, and thecommonly occurring amine acids, e.g., glycine, alanine, phenylalanine,arginine, etc.

Other examples of pharmaceutically acceptable salts include hexanoicacid, cyclopentane propionic acid, pyruvic acid, malonic acid,3-(4-hydroxybenzoyl)benzoic acid, cinnamic acid, 4-chlorobenzenesulfonicacid, 2-naphthalenesulfonic acid, 4-toluenesulfonic acid,camphorsulfonic acid, 4-methylbicyclo-[2.2.2]-oct-2-ene-1-carboxylicacid, 3-phenylpropionic acid, trimethylacetic acid, tertiary butylaceticacid, muconic acid, and the like. The present disclosure alsoencompasses salts formed when an acidic proton present in the parentcompound either is replaced by a metal ion, e.g., an alkali metal ion,an alkaline earth ion, or an aluminum ion; or coordinates with anorganic base such as ethanolamine, diethanolamine, triethanolamine,tromethamine, N-methylglucamine, and the like. In the salt form, it isunderstood that the ratio of the compound to the cation or anion of thesalt can be 1:1, or any ration other than 1:1, e.g., 3:1, 2:1, 1:2, or1:3.

It is to be understood that all references to pharmaceuticallyacceptable salts include solvent addition forms (solvates) or crystalforms (polymorphs) as defined herein, of the same salt.

As used herein, the term “prodrug” refers to any agent which, whenadministered to a mammal, is converted in whole or in part to a targetedcompound (e.g., a β-lactam compound or probenecid described herein). Insome embodiments, the prodrug of a compound (e.g., a β-lactam compoundor probenecid described herein) is also a pharmaceutically acceptablesalt of the compound.

It is to be understood that the compounds of the present disclosure canalso be prepared as esters, for example, pharmaceutically acceptableesters. For example, a carboxylic acid function group in a compound canbe converted to its corresponding ester, e.g., a methyl, ethyl or otherester. Also, an alcohol group in a compound can be converted to itscorresponding ester, e.g., acetate, propionate or other ester.

The compounds, or pharmaceutically acceptable salts thereof, areadministered orally, nasally, transdermally, pulmonary, inhalationally,buccally, sublingually, intraperitoneally, subcutaneously,intramuscularly, intravenously, rectally, intrapleurally, intrathecallyand parenterally. In one embodiment, the compound is administeredorally. One skilled in the art will recognize the advantages of certainroutes of administration.

The dosage regimen utilizing the compounds is selected in accordancewith a variety of factors including type, species, age, weight, sex andmedical condition of the patient; the severity of the condition to betreated; the route of administration; the renal and hepatic function ofthe patient; and the particular compound or salt thereof employed. Anordinarily skilled physician or veterinarian can readily determine andprescribe the effective amount of the drug required to prevent, counter,or arrest the progress of the condition.

Techniques for formulation and administration of the disclosed compoundsof the disclosure can be found in Remington: the Science and Practice ofPharmacy, 19^(h) edition, Mack Publishing Co., Easton, Pa. (1995). In anembodiment, the compounds described herein, and the pharmaceuticallyacceptable salts thereof, are used in pharmaceutical preparations incombination with a pharmaceutically acceptable carrier or diluent.Suitable pharmaceutically acceptable carriers include inert solidfillers or diluents and sterile aqueous or organic solutions. Thecompounds will be present in such pharmaceutical compositions in amountssufficient to provide the desired dosage amount in the range describedherein.

All percentages and ratios used herein, unless otherwise indicated, areby weight. Other features and advantages of the present disclosure areapparent from the different examples. The provided examples illustratedifferent components and methodology useful in practicing the presentdisclosure. The examples do not limit the claimed disclosure. Based onthe present disclosure the skilled artisan can identify and employ othercomponents and methodology useful for practicing the present disclosure.

In the synthetic schemes described herein, compounds may be drawn withone particular configuration for simplicity. Such particularconfigurations are not to be construed as limiting the disclosure to oneor another isomer, tautomer, regioisomer or stereoisomer, nor does itexclude mixtures of isomers, tautomers, regioisomers or stereoisomers;however, it will be understood that a given isomer, tautomer,regioisomer or stereoisomer may have a higher level of activity thananother isomer, tautomer, regioisomer or stereoisomer.

Compounds designed, selected and/or optimized by methods describedabove, once produced, can be characterized using a variety of assaysknown to those skilled in the art to determine whether the compoundshave biological activity. For example, the molecules can becharacterized by conventional assays, including but not limited to thoseassays described below, to determine whether they have a predictedactivity, binding activity and/or binding specificity.

Furthermore, high-throughput screening can be used to speed up analysisusing such assays. As a result, it can be possible to rapidly screen themolecules described herein for activity, using techniques known in theart. General methodologies for performing high-throughput screening aredescribed, for example, in Devlin (1998) High Throughput Screening,Marcel Dekker; and U.S. Pat. No. 5,763,263. High-throughput assays canuse one or more different assay techniques including, but not limitedto, those described below.

All publications and patent documents cited herein are incorporatedherein by reference as if each such publication or document wasspecifically and individually indicated to be incorporated herein byreference. Citation of publications and patent documents is not intendedas an admission that any is pertinent prior art, nor does it constituteany admission as to the contents or date of the same. The inventionhaving now been described by way of written description, those of skillin the art will recognize that the invention can be practiced in avariety of embodiments and that the foregoing description and examplesbelow are for purposes of illustration and not limitation of the claimsthat follow.

EXAMPLES Example 1: Assessment of Probenecid's Effects on PlasmaPharmacokinetic Parameters for β-Lactam Compounds

The effects of probenecid on the pharmoackinetics of sulopneme and itsprodrugs, Compound III-2b and Compound III-1b, were studied in arandomized, double blinded (Investigator and subject blinded,Sponsor-open), placebo-controlled, multiple dose study, with or withoutco administration of probenecid, in fed or fasted state. One hundredninety two subjects were to be randomized to treatment groups to receiveeither active drug or placebo in fed or fasted state with or withoutco-administration of 500 mg probenecid.

Subjects were to be dosed twice a day (every 12 hours) for 6 days and onDay 7 they were to be dosed once. All treatment groups could be run inparallel or sequentially. Subjects were allocated based on therandomization list. Randomization numbers were assigned sequentially assubjects entered into groups on the basis of their order of entry intothe study. Subjects who withdrew for reasons unrelated to safety mayhave been replaced. Blood samples were obtained at prespecifiedintervals in order to characterize pharmacokinetics. Results of thestudy are provided in Tables 1-3.

TABLE 1 Plasma pharmacokinetic parameters - fasted condition(pharmacokinetic population). Compound III-1b + Compound III-2b +Compound III-1b Compound III-2b 500 mg Probenecid 500 mg ProbenecidParameter Number of Subjects (units) 8 8 8 8 Day 1 C_(max) (ng/mL)1998.4 (22.91) 1699.1 (31.64) 2149.4 (27.39) 1720.1 (27.11) T_(max) (h)    1.0000 (0.5000-1.017)     1.0000 (0.4830-2.017)      0.98300(0.5000-1.017)      0.99150 (0.5000-2.017) AUC_(tau) (hr*ng/mL) 2843.7(22.94) 3623.8 (19.19) 4186.1 (23.70) 3857.2 (24.57) TAMIC_(1.0) (h)1.0881 (22.94) 1.0758 (94.61)  1.528 (22.32) 1.1880 (68.73) TAMIC_(0.5)(h) 1.8883 (12.18) 2.6348 (14.85) 2.6550 (18.08) 2.9932 (23.46) Day 7C_(max) (ng/mL) 1247.2 (15.62) 1289.4 (39.17)  2123 (21.91) 1479.5(30.81) T_(max) (h)     1.0000 (0.4830-1.017)      0.99150(0.5000-1.033)      0.99150 (0.5000-1.017)     1.2500 (0.5000-2.967)AUC_(last) (hr*ng/mL) 1866.7 (25.01) 2607.4 (19.10) 4363.8 (29.02)4236.5 (26.91) AUC_(inf) (hr*ng/mL) 1890.3 (24.38) 2627.8 (18.89) 4412.5(28.98) 4282.7 (27.06) AUC_(tau) (hr*ng/mL) 1889.9 (24.38) 2626.3(18.89) 4402.5 (28.77) 4276.4 (26.99) t_(1/2) (h)¹ 0.78443 (25.88) 0.93761 (15.34)  1.2208 (18.14) 1.0747 (16.36) TAMIC_(1.0) (h) 0.54586(65.52)  0.73202 (62.70)  1.6161 (28.85) 1.3240 (84.30) TAMIC_(0.5) (h)1.4528 (17.74) 2.1088 (16.74) 2.8875 (21.76) 3.4394 (23.07) ¹Displayedfor Day 7 only. T_(max) reported as Median (minimum-maximum). AUC_(inf)= the area under the concentration time curve extrapolated to infinity;AUC_(last) = AUC from time 0 to the time of the last (Day 1)quantifiable concentration; AUC_(tau) = area under the concentrationtime curve from time 0 to 12 hours; % CV = coefficient of variation;C_(max) = maximum observed concentration; SD = standard deviation;t_(1/2) = terminal half-life; T_(max) = time to maximum observedconcentration

TABLE 2 Plasma pharmacokinetic parameters - fed condition(pharmacokinetic population). Compound III-1b + Compound III-2b +Compound III-1b Compound III-2b 500 mg Probenecid 500 mg ProbenecidParameter Number of Subjects (units) 8 8 8 8 Day 1 C_(max) (ng/mL)1434.5 (23.98) 1730.9 (46.66) 1567.9 (30.31) 1615.5 (31.86) T_(max) (h)    0.9830 (1.0000-1.500)       1.000 (1.5000-2.983)     0.9830(1.0170-5.950)     0.5000 (1.7415-4.000) AUC_(tau) (hr*ng/mL) 3274.6(23.02) 4413.7 (27.00) 4128.2 (18.58) 6255.2 (23.16) TAMIC_(1.0) (h) 1.180 (43.27) 2.0882 (25.12) 1.6543 (32.68) 2.0925 (46.59) TAMIC_(0.5)(h) 2.5810 (16.07) 3.0103 (31.13) 3.1035 (16.11) 5.0404 (37.07) Day 7C_(max) (ng/mL) 1204.9 (31.04) 1179.4 (25.94) 1791.3 (23.50) 1586.5(23.42) T_(max) (h)     0.9830 (1.0165-2.000)       1.483 (2.0000-4.000)      1.000 (1.2420-2.000)       1.000 (2.5000-4.017) AUC_(last)(hr*ng/mL) 2776.6 (23.17)  3537 (25.01) 4452.7 (23.32) 6591.3 (26.35)AUC_(inf) (hr*ng/mL) 2804.9 (22.94) 3712.7 (24.27) 4521.8 (23.42) 6679.8(26.42) AUC_(tau) (hr*ng/mL) 2803.6 (22.95) 3706.4 (24.21) 4512.9(23.41) 6631.2 (25.87) t_(1/2) (h)¹ 0.92384 (11.91)  0.91139 (26.68) 1.1311 (12.87) 1.2174 (30.84) TAMIC_(1.0) (h) 0.46944 (290.26) 1.3191(62.54) 1.8174 (28.00) 2.7087 (42.70) TAMIC_(0.5) (h) 2.2883 (19.01)2.8507 (31.48) 3.1532 (14.59) 5.1164 (26.75) ¹Displayed for Day 7 only.T_(max) is reported as Median (minimum-maximum). AUC_(inf) = the areaunder the concentration time curve extrapolated to infinity; AUC_(last)= AUC from time 0 to the time of the last (Day 1) quantifiableconcentration; AUC_(tau) = area under the concentration time curve fromtime 0 to 12 hours; % CV = coefficient of variation; C_(max) = maximumobserved concentration; SD = standard deviation; t_(1/2) = terminalhalf-life; T_(max) = time to maximum observed concentration

TABLE 3 Statistical assessment of probenecid effect on plasmapharmacokinetic parameters (pharmacokinetic population). WithProbenecid/ Without Probenecid With Probenecid Without Probenecid VisitParameter N¹ GM 95% CI N¹ GM 95% CI GMR 90% CI Compound III-1b Day 1C_(max) (ng/mL) 16 1693.11 (1452.31, 16 1835.76 (1574.68, 1.08 (0.91,1.30) 1973.83) 2140.14) AUC_(tau) 16 3051.54 (2728.68, 15 4158.98(3705.34, 1.36 (1.19, 1.56) (h · ng/mL) 3412.61) 4668.16) Day 7 C_(max)(ng/mL) 16 1225.85 (1088.01, 16 1950.08 (1730.81, 1.59 (1.38, 1.83)1381.14) 2197.12) AUC_(tau) 16 2301.85 (1997.29, 16 4457.34 (3867.58,1.94 (1.64, 2.29) (h.ng/mL) 2652.85) 5137.03) Compound III-2b Day 1C_(max) (ng/mL) 16 1714.92 (1450.13, 16 1667.01 (1409.62, 0.97 (0.80,1.18) 2028.06) 1971.40) AUC_(tau) 16 3999.26 (3439.92, 16 4911.98(4224.99, 1.23 (1.03, 1.47) (hr * ng/mL) 4649.54) 5710.68) Day 7 C_(max)(ng/mL) 16 1233.18 (1063.71, 16 1532.10 (1321.56, 1.24 (1.04, 1.48)1429.64) 1776.18) AUC_(tau) 15 3084.36 (2621.79, 16 5325.20 (4549.98,1.73 (1.43, 2.08) (hr * ng/mL) 3628.54) 6232.50) ¹Shows the number ofsubjects exposed to each treatment that was used in the linear model.AUC_(tau) = area under the concentration time curve from time 0 to 12hours; CI = confidence intervals; C_(max) = maximum observedconcentration; GM = geometric means; GM = ratio of geometric means

A Phase 1, randomized, investigator-blind, subject-blind, sponsor-open,placebo-controlled, single and multiple dose study of Compound III-2bwas further conducted. There were 6 planned cohorts of subjects. Eachcohort was planned to enroll 12 subjects, for a total of 72 plannedsubjects. Subjects in the multidose cohort were dosed for 10 days; newsubjects were recruited for each cohort. Results from cohorts 2 and 3,provided in Table 4 are provided below. Subjects in these cohorts, onDays 1 through 9, were dosed BID (12 hours apart) at approximately 0800and 2000 hours. On Day 10, subjects were to be dosed only once atapproximately 0800 hours. Blood samples were obtained at prespecifiedintervals in order to characterize pharmacokinetics.

TABLE 4 Plasma pharmacokinetic parameters following administration ofCompound III-2b with and without probenecid. Compound III-2b 1200mg/Probenecid Compound III-2b Parameter^(a) 1000 mg BID 2000 mg BIDStudy Day 1; Plasma N, n 9, 8 9, 9 AUC_(inf) (ng · hr/mL) 20400 (24)18100 (26) AUC_(tau) (ng · hr/mL) 20000 (21) 17500 (24) C_(max) (ng/mL)6520 (25) 6090 (19) T_(max) (hr) 1.00 (1.00-3.00) 1.00 (1.00-2.00)T_(last) (hr) 8.00 (6.00-12.00) 8.00 (8.00-12.00) t_(1/2) (hr) 2.09 (63)1.66 (50) TAMIC1 7.01 (30) 6.93 (34) TAMIC2 5.48 (32) 5.57 (28) StudyDay 10; Plasma N, n 9, 6 9, 8 AUC_(inf) (ng · hr/mL) NC NC AUC_(tau) (ng· hr/mL) 18800 (18) 12200 (21) C_(max) (ng/mL) 6660 (23) 5480 (18)T_(max) (hr) 1.30 (1.00-2.00) 1.00 (1.00) C_(trough) (ng/mL) 13.44 (83)0.00 (283) T_(last) (hr) 8.00 (8.00-12.00) 8.00 (6.00-12.00) t_(1/2)(hr) 1.44 (14) 1.27 (26) TAMIC1 6.35 (11) 4.70 (24) TAMIC2 4.74 (11)3.61 (24) Rac 0.892 (9) 0.685 (18) Study Day 6; Urine Ae₂₄ (ug) 139000(30) 253000 (26) (N = 9, n = 8) (N = 9, n = 9) Ae % (%) 16.2 (29) 17.3(26) (N = 9, n = 8) (N = 9, n = 9) CL/R (mL/hr) 7.77 (21) 22.0 (25) (N =9, n = 6) (N = 9, n = 8) ^(a)Geometric mean (% CV) for AUC_(inf),AUC_(tau), C_(max), and CL/R; arithmetic mean (% CV) for t½, AE %;median (range) for T_(max), T_(last), TAMIC1, and TAMIC2. AE₂₄ = amountof sulopenem excreted unchanged in urine over 24 hours post doseadministration, AE % = percent of sulopenem dose excreted in urine,AUC_(inf) = area under the concentration-time curve from time 0 toinfinite time, AUC_(tau) = area under the concentration-time curve fromtime 0 to time_(τ) (the dosing interval), BID = twice daily, CL/R =renal clearance, C_(max) = maximum (peak) observed drug concentrationafter single dose administration, C_(trough) = minimum (trough) observeddrug concentration, MIC_(0.5) = time above the duration of plasmaconcentrations exceeding 0.5 μg/mL, MIC_(1.0) = time above the durationof plasma concentrations exceeding 1.0 μg/mL, N = number of subjects; n= number of subjects contributing to the mean, NC = summary statisticsnot calculated, Rac = accumulation ratio, t½ = elimination half-life,TAMIC1 = time above minimum inhibitory concentration, when minimumconcentration is 0.5 μg/mL, TAMIC2 = time above minimum inhibitoryconcentration, when minimum concentration is 1.0 μg/mL, T_(max) = timeto reach peak or maximum concentration following drug administration.

Example 2: Comparison of Probenecid's Effects on Plasma PharmacokineticParameters for β-Lactam Compounds by Oral Administration and ContinuousInfusion

The pharmacokinetics of Compound III-2b were studies in a randomized,subject-blinded, investigator- and sponsor-open, placebo-controlled,multiple-dose study, run in parallel cohorts. There were 7 cohorts ofapproximately 10 subjects each (4:1 active:placebo). Subjects were dosedBID (every 12 hours) for 6 days and on Day 7 they were dosed only once.Blood samples were obtained at prespecified intervals in order tocharacterize pharmacokinetics. Results are provided in Table 5.

TABLE 5 Geometric mean (CV %) of plasma pharmacokinetic parameters -oral administration. Cohorts (Treated with Compound III-2b) 1 2 3 4 6 7Parameter (units) N = 8 N = 8 N = 8 N = 8 N = 8 N = 8 Day 1 Number ofSubjects, n 8   6   5   8   8   7   C_(max) (ng/mL) 4420 (24) 2760 (13)3700 (42) 1470 (34)  2950 (22) 3320 (36) AUC_(inf) (ng · h/mL) 9430 (13)6680 (20) 12900 (23)  3400 (20) 11000 (25) 8290 (6)  AUC_(last) (ng ·h/mL) 9330 (13) 6770 (22) 12100 (21)  3260 (22) 10800 (26) 7670 (13)T_(max) ^(a) (h) 1.50 1.50 2.50 1.03 2.50 1.75 [1.05-4.00] [0.50-6.03][1.50-4.00] [0.50-2.00] [1.00-4.00] [1.00-6.00] t½^(b) (h) 0.823 (13)  1.37 (33)  1.20 (14) 0.862 (19)    1.23 (13)  1.26 (40) TAMIC_(0.5)^(a) (h) 4.35 3.69 6.34 2.66 6.52 4.90 [3.19-5.76] [3.09-7.04]4.54-9.39] [2.15-4.35] [5.31-7.34] [2.91-5.77] TAMIC_(1.0) ^(a) (h) 3.212.91 4.81 1.38 4.80 3.32 [2.31-4.98] [1.90-4.69] [2.92-6.91] [0.00-1.67][2.88-5.40] [2.29-3.63] Day 7 Number of Subjects, n 8   7   6   7   8  6   C_(max) (ng/mL) 3770 (23) 2410 (33) 2670 (28) 1310 (22)  3300 (16)2090 (28) AUC_(inf) (ng · h/mL) 7800 (17) 6020 (16) 9950 (15) 2990 (23)11900 (24) 6750 (11) AUC_(last) (ng · h/mL) 7670 (17) 6070 (19) 9710(15) 2730 (27) 11500 (24) 6230 (16) T_(max) ^(a) (h) 2.00 1.75 2.51 1.502.00 4.00 [1.50-3.00] [1.00-6.00] [1.00-4.00] [0.50-3.02] [1.00-4.00][2.00-6.00] t½^(b) (h) 0.761 (11)   1.08 (24) 0.901 (14)  0.797 (16)   1.50 (17) 0.790 (2)   R_(ac) ^(b) 0.832 (13)  0.910 (11)  0.809 (14) 0.873 (29)    1.10 (24) 0.827 (21)  TAMIC_(0.5) ^(a) (h) 3.32 4.18 5.962.38 6.26 4.62 [2.85-5.02] [2.76-6.96] [4.54-6.75] [1.30-3.72][4.70-7.36] [4.43-4.89] TAMIC_(1.0) ^(a) (h) 2.64 2.72 4.44  0.803 4.673.22 [2.10-4.22] [1.95-3.17] [3.23-5.47] [0.00-2.13] [3.00-5.85][1.69-3.94] Ae24^(b,c) (mg) 138.7 (27)   74.4 (23) Ae24%^(b,c, d) (%) 19.0 (27)  10.2 (23) CLr^(b,c) (L/h)  17.4 (19)  12.2 (30) ^(a)Median(range). ^(b)Arithmetic mean (CV %). ^(c)Collected for Cohorts 1 and 2only. ^(d)Ratio was adjusted for the MW difference between sulopenem (MW= 349.45) and Compound III-2b (MW = 477.62). Cohort 1 was CompoundIII-2b 1 g BID in the fed state. Cohort 2 was Compound III-2b 1 g BID inthe fasted state. Cohort 3 was Compound III-2b 1.5 g BID in the fedstate. Cohort 4 was Compound III-2b 0.5 g BID in the fasted state.Cohort 6 was Compound III-2b 1 g plus probenecid 1 g BID in the fastedstate. Cohort 7 was Compound III-2b 1 g TID in the fed state. N = thetotal number of subjects in the treatment group in the indicatedpopulation. n = the number of subjects with estimable AUC_(inf) and t½.CV = coefficient of variation; C_(max) = maximum observed plasmaconcentration within the dosing interval; AUC_(inf) = area under theplasma concentration-time curve from time 0 extrapolated to infinitetime; AUC_(last) = area under the plasma concentration-time curve fromtime 0 to time of the last quantifiable concentration; T_(max) = time toC_(max); t½ = elimination half-life; TAMIC_(0.5) = duration of timeplasma drug concentrations exceeded 0.5 μg/mL; TAMIC_(1.0) = duration oftime plasma drug concentrations exceeded 1.0 μg/mL; R_(ac) =accumulation ratio; Ae24 = amount of unchanged drug excreted in urineover 24 hours postdose; Ae24% = cumulative amount of unchanged drugrecovered in the urine up to time 24-hour postdose, expressed as apercent of administered dose; CL_(r) = renal clearance; BID = twicedaily; TID = 3 times daily; MW = molecular weight.

The pharmacokinetics of sulopenem delivered intravenously were studiedin a randomized, investigator-blind, subject-blind, sponsor-open,placebo-controlled, multiple-dose study of sulopenem. There were 5cohorts dosed. Each subject was dosed for up to 14 days. Each cohortconsisted of 10 subjects. Blood samples were obtained at prespecifiedintervals in order to characterize pharmacokinetics. Results areprovided in Table 6.

TABLE 6 Geometric mean (CV %) of plasma pharmacokinetic parameters -continuous infusion. 800 mg 1200 mg 1600 mg 1200 mg 2000 mg Parameter (3h BID) (1 h BID) (1.5 h BID) (2.5 h BID) (1.5 h BID) (units)^(a) N = 8 N= 8 N = 8 N = 8 N = 8 Day 1 C_(max) (ng/mL)  7270 (21) 32500 (41) 40100(14) 16600 (11) 51500 (16) AUC_(inf) (ng · hr/mL) 22400 (20) 42300 (29)67300 (13) 41900 (11) 90300 (17) AUC_(last) (ng · hr/mL) 22300 (20)42200 (29) 67100 (13) 41800 (11) 90100 (17) T_(max) ^(b) (hr) 2.00[2.00-3.00] 1.00 [1.00-1.00] 1.50 [1.00-1.50] 2.25 [2.00-2.50] 1.50[1.00-1.50] t_(1/2) ^(c) (hr)  0.825 (19)  1.04 (9)  1.04 (12)  1.12 (8) 1.12 (26) TAMIC0.5 μg/mL^(b) (h) 4.99 [4.79-5.53] 4.93 [4.28-5.94] 5.61[5.22-6.41] 5.59 [4.83-6.63] 6.47 [5.59-7.08] TAMIC1.0 μg/mL^(b) (h)4.47 [4.12-4.68] 3.86 [3.54-4.64] 4.67 [3.99-4.99] 4.74 [4.15-5.57] 5.39[4.62-6.20] Day 14 C_(max) (ng/mL)  8970 (17) 30700 (16) 31800 (12)13500 (11) NE AUC_(inf) (ng · hr/mL) 26500 (15) 41400 (17) 54900 (11)34600 (10) AUC_(last) (ng · hr/mL) 26400 (15) 41300 (17) 54700 (12)34500 (10) NE T_(max) ^(b) (hr) 2.00 [2.00-3.00] 1.00 [1.00-1.00] 1.25[1.00-1.50] 2.00 [2.00-2.50] NE t_(1/2) ^(c) (hr)  0.889 (15)  1.05 (20) 1.20 (10)  1.01 (26) NE R_(ac) ^(c)  1.15 (29)  0.928 (17) 0.791 (9) 0.841 (9)  NE TAMIC0.5 μg/mL^(a) (h) 5.05 [4.88-5.72] 4.67 [3.78-6.47]5.77 [4.19-6.09] 4.79 [4.59-5.38] NE TAMIC1.0 μg/mL^(a) (h) 4.42[4.31-4.66] 3.63 [3.16-5.22] 4.45 [3.73-4.62] 3.96 [3.84-4.62] NE Ae₂₄^(c) (mg)  406 (17)  614 (19)  1080 (14)  643 (10) NE Ae₂₄ ^(c) (%) 50.8 (17)  51.1 (19)  67.4 (14)  53.6 (10) NE CL_(r) ^(c) (L/hr)  15.4(18)  14.7 (13)  19.6 (14)  18.8 (17) NE ^(a)Pharmacokinetic parametersare defined in Tables 1-5. ^(b)median [range] ^(c)arithmetic mean (CV%)] BID = twice daily, h = hours, CV = coefficient of variation, NE =not estimated, study stopped before Day 14 assessment, TAMIC0.5 =duration of plasma sulopenem concentrations exceeding 0.5 μg/mL,TAMIC1.0 = duration of plasma sulopenem concentrations exceeding 1.0μg/mL.

Example 3: Summary of Various Studies in Examples 1 and 2

The results of various studies described in Examples 1 and 2 weresummarized in Tables 7A-7C below, which were further summarized inFIG. 1. It was observed that, when Compound III-1b or Compound III-2bwas administered alone through the oral route, the AUC of sulopenem onDay 7 was lower than that on Day 1. Further, it was observed that, whenCompound III-1b or Compound III-2b was co-administered with probenecid,the AUC of sulopenem was increased on Day 7 beyond that seen on Day 1.

TABLE 7A Plasma pharmacokinetic parameters following administration ofCompound III-1b or Compound III-2b with and without probenecid (based onTables 1 and 3 in Example 1). Compound Compound III-1b + III-2b +Parameter Compound 500 mg Compound 500 mg (units) III-1b ProbenecidIII-2b Probenecid Day 1 AUC_(tau) 2843.7 4186.1 3623.8 3857.2 (hr*ng/mL)Day 7 AUC_(tau) 1889.9 4402.5 2626.3 4276.4 (hr*ng/mL) Day 1-Day 7AUC_(tau) −953.8 216.4 −1000.5 419.2 difference (−33.5%) (5.2%) (27.6%)(10.9%) (hr*ng/mL) (%) AUC_(tau) = area under the concentration timecurve from time 0 to 12 hours.

TABLE 7B Plasma pharmacokinetic parameters following administration ofCompound III-2b with and without probenecid (based on Table 4 of Example1). Compound Compound III-2b Parameter III-2b (1200 mg) + (units) (2000mg) Probenecid Day 1 AUC_(tau) (hr*ng/mL) 17500 20000 Day 10 AUC_(tau)(hr*ng/mL) 12200 18800 Day 1-Day 10 AUC_(tau) difference −5300 −1200(hr*ng/mL) (%) (−30.3%) (−6.0%) AUC_(tau) = area under the concentrationtime curve from time 0 to 12 hours.

TABLE 7C Plasma pharmacokinetic parameters following administration ofvarious doses of Compound III-2b with and without probenecid (based onTable 5 in Example 2). Compound Compound Compound Compound CompoundIII-2b Compound III-2b III-2b III-2b Parameter III-2b (1000 mg) + III-2b(1000 mg) (500 mg) (1000 mg) (units) (1000 mg) Probenecid (1500 mg) FEDFED TID FED Day 1 AUC_(inf) (hr * ng/mL) 6680 11000 12900 9430 3400 8290Day 7 AUC_(inf) (hr * ng/mL) 6020 11900  9950 7800 2990 6750 Day 1 − Day7 AUC_(inf) difference −660  900 −2950 −1630  −410 −1540  (hr * ng/mL)(%) (−9.9%) (8.2%) (22.9%) (−17.3%) (−12.1%) (−18.6%) AUC_(inf) = thearea under the concentration time curve extrapolated to infinity.

Example 4: Effects of Administrating β-Lactam Compounds and Probenecidby the Same Administration Route

Normal and healthy subjects were given the β-lactam compound (CompoundIII-2b; sulopenem etzadroxil) and probenecid in two separate studies. InStudy No. 1, subjects were administered 500 mg of sulopenem etzadroxilas a powder for oral suspension and simultaneously dosed with 500 mg ofprobenecid provided as a monolayer tablet. In Study No. 2, subjects wereadministered 500 mg of sulopenem etzadroxil with 500 mg of probenecid inan oral co-formulation. The results of the two studies are shown inFIGS. 2-5 and Table 8 below.

TABLE 8 Comparison of AUC in subjects given sulopenem etzadroxil andprobenecid AUC_(last) ng · hr/ml Fasted Fed Study No. 1 4325.9 6592.8Study No. 2 5099.5 7336.4 Difference (% Increase) 773.6 (17.9%) 743.6(11.3%)

It is observed that administration of sulopenem etzadroxil andprobenecid in the co-formulation results in an increase in the amount ofsulopenem in the blood relative to dosing each agent in a separateformulation.

Administration in the fasted state of a combination of sulopenemetzadroxil and probenecid in the co-formulation results in a 17.9%increase in the amount of sulopenem in the blood, as measured by thearea under the curve, relative to the same amount of sulopenemetzadroxil delivered as powder in a bottle administered with probenecidin a monolayer tablet.

Similarly, the administration in the fed state of a combination ofsulopenem etzadroxil and probenecid in the co-formulation results in a11.3% increase in the amount of sulopenem in the blood, as measured bythe area under the curve, relative to the same amount of sulopenemetzadroxil delivered as powder in a bottle administered with probenecidin a monolayer tablet.

EQUIVALENTS

It is to be understood that the invention can be embodied in otherspecific forms without departing from the spirit or essentialcharacteristics thereof. The foregoing embodiments are therefore to beconsidered in all respects illustrative rather than limiting on theinvention described herein. Scope of the invention is thus indicated bythe appended claims rather than by the foregoing description, and allchanges that come within the meaning and range of equivalency of theclaims are intended to be embraced therein.

1. A method of treating or preventing a disease, comprisingadministering to a subject in need thereof a pharmaceutically effectiveamount of a β-lactam compound or a pharmaceutically acceptable saltthereof and probenecid or a pharmaceutically acceptable salt thereof,wherein the β-lactam compound or the pharmaceutically acceptable saltthereof and probenecid or the pharmaceutically acceptable salt thereofare administered by the same administration route.
 2. The method ofclaim 1, wherein the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are administered simultaneously.
 3. The methodof claim 1, wherein the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof are both administered by enteral administration.4. The method of claim 3, wherein the enteral administration is oraladministration.
 5. The method of claim 1, wherein an oral co-formulationcomprising the β-lactam compound or the pharmaceutically acceptable saltthereof and probenecid or the pharmaceutically acceptable salt thereofis administered.
 6. The method of claim 5, wherein a tablet comprisingthe β-lactam compound or the pharmaceutically acceptable salt thereofand probenecid or the pharmaceutically acceptable salt thereof isadministered. 7.-8. (canceled)
 9. The method of claim 1, wherein theβ-lactam compound or the pharmaceutically acceptable salt thereof andprobenecid or the pharmaceutically acceptable salt thereof are bothadministered by parenteral administration.
 10. The method of claim 9,wherein the parenteral administration is intravenous administration. 11.The method of claim 1, wherein the administration results in a plasmaconcentration for the β-lactam compound having an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.
 12. The method of claim1, wherein the administration results in a plasma concentration for theβ-lactam compound having an area under the curve (AUC) that is higher inthe subject in need thereof as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes by about 5% or greater, about 10% or greater,about 15% or greater, about 20% or greater, about 25% or greater, about30% or greater, about 40% or greater, about 50% or greater, about 60% orgreater, about 80% or greater, about 100% or greater, about 150% orgreater, about 200% or greater, about 300% or greater, about 400% orgreater, or about 500% or greater within about 30 minutes, about 1 hour,about 2 hours, about 3 hours, about 6 hours, about 12 hours, about 18hours, about 1 day, about 2 days, about 3 days, about 4 days, about 5days, about 6 days, or about 7 days from the administration. 13.(canceled)
 14. The method of claim 1, wherein the administration resultsin a plasma concentration for the β-lactam compound having a maximumplasma concentration (C_(max)) in the subject in need thereof that isfrom about 50% to about 150%, from about 60% to about 140%, from about70% to about 130%, from about 80% to about 120%, from about 90% to about110%, from about 95% to about 105%, or from 98% to about 102% ascompared to a comparable subject being administered with the β-lactamcompound and probenecid by different administration routes.
 15. Themethod of claim 1, wherein the administration results in a plasmaconcentration for the β-lactam compound having a maximum plasmaconcentration (C_(max)) in the subject in need thereof that issubstantially the same as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes.
 16. The method of claim 1, wherein theadministration results in a plasma concentration for the β-lactamcompound having: an area under the curve (AUC) that is higher in thesubject in need thereof as compared to a comparable subject beingadministered with the β-lactam compound and probenecid by differentadministration routes by about 20% or greater within about 1 day fromthe administration; and a maximum plasma concentration (C_(max)) in thesubject in need thereof that is substantially the same as compared to acomparable subject being administered with the β-lactam compound andprobenecid by different administration routes.
 17. The method of claim1, wherein about 500 mg of the β-lactam compound or the pharmaceuticallyacceptable salt and about 500 mg of the probenecid or thepharmaceutically acceptable salt are administered to the subject in needthereof, and the administration results in a plasma concentration forthe β-lactam compound having: an area under the curve (AUC) being fromabout 4100 ng·h/mL to about 5500 ng·h/mL, from about 4200 ng·h/mL toabout 5400 ng·h/mL, from about 4300 ng·h/mL to about 5300 ng·h/mL, fromabout 4400 ng·h/mL to about 5200 ng·h/mL, from about 4500 ng·h/mL toabout 5100 ng·h/mL, from about 4650 ng·h/mL to about 5000 ng·h/mL, fromabout 4750 ng·h/mL to about 4900 ng·h/mL, or from about 4800 ng·h/mL toabout 4850 ng·h/mL within about 12 hours from the administration; and amaximum plasma concentration (C_(max)) being from about 1100 ng/mL toabout 2500 ng/mL, from about 1200 ng/mL to about 2400 ng/mL, from about1300 ng/mL to about 2300 ng/mL, from about 1400 ng/mL to about 2200ng/mL, from about 1500 ng/mL to about 2100 ng/mL, from about 1650 ng/mLto about 2000 ng/mL, from about 1750 ng/mL to about 1900 ng/mL, or fromabout 1800 ng/mL to about 1850 ng/mL.
 18. The method of claim 1, whereinabout 500 mg of the β-lactam compound or the pharmaceutically acceptablesalt and about 500 mg of the probenecid or the pharmaceuticallyacceptable salt are administered to the subject in need thereof, and theadministration results in a plasma concentration for the β-lactamcompound having: an area under the curve (AUC) being from about 7000ng·h/mL to about 8400 ng·h/mL, from about 7100 ng·h/mL to about 8300ng·h/mL, from about 7200 ng·h/mL to about 8200 ng·h/mL, from about 7300ng·h/mL to about 5100 ng·h/mL, from about 7450 ng·h/mL to about 8100ng·h/mL, from about 7500 ng·h/mL to about 8050 ng·h/mL, or from about7550 ng·h/mL to about 8000 ng·h/mL within about 12 hours from theadministration; and a maximum plasma concentration (C_(max)) being fromabout 2100 ng/mL to about 3300 ng/mL, from about 2200 ng/mL to about3200 ng/mL, from about 2300 ng/mL to about 3100 ng/mL, from about 2400ng/mL to about 3000 ng/mL, from about 2500 ng/mL to about 2900 ng/mL,from about 2550 ng/mL to about 2800 ng/mL, from about 2600 ng/mL toabout 2750 ng/mL, or from about 2650 ng/mL to about 2700 ng/mL.
 19. Themethod of claim 1, wherein a food is administered to the subject duringthe administration of the β-lactam compound or the pharmaceuticallyacceptable salt thereof and probenecid or the pharmaceuticallyacceptable salt thereof.
 20. The method of claim 19, wherein theadministration results in a plasma concentration for the β-lactamcompound having an area under the curve (AUC) that is higher in thesubject in need thereof as compared to a comparable subject beingadministered with the β-lactam compound and probenecid without the food.21. A method of treating or preventing a disease, comprisingadministering to a subject in need thereof a pharmaceutically effectiveamount of a β-lactam compound or a pharmaceutically acceptable saltthereof and probenecid or a pharmaceutically acceptable salt thereofover a period of time, wherein the administration results in a plasmaconcentration for the β-lactam compound having: an area under the curve(AUC) that is higher in the subject in need thereof as compared to acomparable subject being administered to the pharmaceutically effectiveamount of the β-lactam compound without probenecid over the period oftime, a maximum plasma concentration (C_(max)) that is higher in thesubject in need thereof as compared to the comparable subject beingadministered to the pharmaceutically effective amount of the β-lactamcompound without probenecid over the period of time, or a combinationthereof.
 22. The method of claim 21, wherein the period of the time islonger than about 24 hours
 23. The method of claim 21, wherein one orboth of the AUC and C_(max) of the plasma concentration for the β-lactamcompound in the subject in need thereof is observed at a time beingafter about the first 24 hours of the administration. 24.-44. (canceled)45. The method of claim 21, wherein the administration of the probenecidor a pharmaceutically acceptable salt thereof enhances the absorptionrate of the β-lactam compound or a pharmaceutically acceptable saltthereof in the subject in need thereof. 46.-47. (canceled)
 48. Themethod of claim 1, wherein the subject in need thereof is a human.49.-50. (canceled)
 51. The method of claim 1, wherein the disease isassociated with an infection. 52.-54. (canceled)
 55. The method of claim51, wherein the infection is resistant to one or more β-lactam compoundswhen being administered without probenecid or the pharmaceuticallyacceptable salt thereof.
 56. The method of claim 1, wherein the diseaseis an uncomplicated urinary tract infection, a complicated urinary tractinfection, a complicated intra-abdominal infection, pneumonia, otitismedia, sinusitis, gonococcal urethritis, pelvic inflammatory disease,prostatitis, bone infection, joint infection, diabetic foot infectionand infectious diarrhea.
 57. (canceled)
 58. The method of claim 1,wherein the β-lactam compound is any one of Formula (I), (Ia), and (Ib):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R¹ is H or optionallysubstituted alkyl. 59.-65. (canceled)
 66. The method of claim 1, whereinthe β-lactam compound is of any one of Formulae (III), (IIIa), and(IIIb):

a pharmaceutically acceptable salt thereof, a prodrug thereof, an analogthereof, or a derivative thereof, wherein R² is H or optionallysubstituted alkyl.
 67. (canceled)
 68. The method of claim 1, wherein theβ-lactam compound is selected from the group consisting of:

pharmaceutically acceptable salts thereof, prodrugs thereof, analogsthereof, and derivatives thereof. 69.-141. (canceled)
 142. Apharmaceutical composition comprising a β-lactam compound or apharmaceutically acceptable salt thereof and probenecid or apharmaceutically acceptable salt thereof. 143.-145. (canceled)
 146. Acompound or a pharmaceutical salt thereof, wherein administration of thecompound or the pharmaceutical salt thereof in combination withprobenecid or a pharmaceutically acceptable salt thereof into a subjectin need thereof over a period of time results in a plasma concentrationversus time curve for the compound having: an area under the curve (AUC)that is higher in the subject in need thereof as compared to acomparable subject being administered to the pharmaceutically effectiveamount of the compound without probenecid over the period of time, amaximum plasma concentration (C_(max)) for the compound that is higherin the subject in need thereof as compared to the comparable subjectbeing administered to the pharmaceutically effective amount of thecompound without probenecid over the period of time, or a combinationthereof.